67b5d2aa9a
This massive set of changes was triggered by issue #546. In addition to the better handling of !weak, this also adds some weak properties in a few places. * spot/twaalgos/product.cc (product_aux): Throw some exception if an automaton with t or f acceptance has the !weak property. This is a cheap sanity check to help detect algorithms that incorrectly assumed !weak input would necessarily become !weak output. * spot/twaalgos/hoa.cc (print_hoa): Likewise, also do not assume that terminal implies very-weak. * spot/parseaut/parseaut.yy: Add several diagnostics for similar cases. E.g., a one-state automaton cannot be declared as !very-weak. * tests/core/parseaut.test: Check those new diagnostics. * spot/twa/twa.cc (twa::intersecting_run): Temporary remove the weak property by setting it to maybe, not to false. * spot/twaalgos/minimize.cc, spot/twaalgos/parity.cc, spot/twaalgos/sccfilter.cc, spot/twaalgos/simulation.cc: Account for the fact that these algorithm may in fact improve the weakness. * spot/twaalgos/strength.cc: Only look at colors used by the acceptance condition when deciding weakness. * spot/twaalgos/synthesis.cc: Declare the strategy as weak. * bin/randaut.cc: Add weak to automata with t/f acceptance. * spot/kripke/kripke.hh: Make kripke structures as weak. * tests/core/acc_word.test, tests/core/alternating.test, tests/core/complement.test, tests/core/complete.test, tests/core/ltlsynt.test, tests/core/randomize.test, tests/core/readsave.test, tests/core/remfin.test, tests/core/sccsimpl.test, tests/core/strength.test, tests/core/wdba2.test, tests/ltsmin/kripke.test, tests/python/automata-io.ipynb, tests/python/automata.ipynb, tests/python/dbranch.py, tests/python/highlighting.ipynb, tests/python/kripke.py, tests/python/ltsmin-dve.ipynb, tests/python/mealy.py, tests/python/simstate.py: Adjust all these test cases. * NEWS: Mention the fixes.
2132 lines
139 KiB
Text
2132 lines
139 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\n",
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"import spot.ltsmin\n",
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"# The following line causes the notebook to exit with 77 if divine is not \n",
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"# installed, therefore skipping this test in the test suite.\n",
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"spot.ltsmin.require('divine')\n",
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"# This notebook also tests the limitation of the number of states in the GraphViz output\n",
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"spot.setup(max_states=10)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"There are two ways to load a DiVinE model: from a file or from a cell. \n",
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"\n",
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"Loading from a file\n",
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"-------------------\n",
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"\n",
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"We will first start with the file version, however because this notebook should also be a self-contained test case, we start by writing a model into a file."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"!rm -f test1.dve"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Writing test1.dve\n"
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]
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}
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],
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"source": [
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"%%file test1.dve\n",
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"int a = 0, b = 0;\n",
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"\n",
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"process P {\n",
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" state x;\n",
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" init x;\n",
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"\n",
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" trans\n",
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" x -> x { guard a < 3 && b < 3; effect a = a + 1; },\n",
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" x -> x { guard a < 3 && b < 3; effect b = b + 1; };\n",
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"}\n",
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"\n",
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"process Q {\n",
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" state wait, work;\n",
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" init wait;\n",
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" trans\n",
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" wait -> work { guard b > 1; },\n",
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" work -> wait { guard a > 1; };\n",
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"}\n",
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"\n",
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"system async;"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The `spot.ltsmin.load` function compiles the model using the `ltlmin` interface and load it. This should work with DiVinE models if `divine --LTSmin` works, and with Promela models if `spins` is installed."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"m = spot.ltsmin.load('test1.dve')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Compiling the model creates all several kinds of files. The `test1.dve` file is converted into a C++ source code `test1.dve.cpp` which is then compiled into a shared library `test1.dve2c`. Because `spot.ltsmin.load()` has already loaded this shared library, all those files can be erased. If you do not erase the files, `spot.ltsmin.load()` will use the timestamps to decide whether the library should be recompiled or not everytime you load the library.\n",
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"\n",
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"For editing and loading DVE file from a notebook, it is a better to use the `%%dve` as shown next."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"!rm -f test1.dve test1.dve.cpp test1.dve2C"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Loading from a notebook cell\n",
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"----------------------------\n",
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"\n",
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"The `%%dve` cell magic implements all of the above steps (saving the model into a temporary file, compiling it, loading it, erasing the temporary files). The variable name that should receive the model (here `m`) should be indicated on the first line, after `%dve`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"%%dve m\n",
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"int a = 0, b = 0;\n",
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"\n",
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"process P {\n",
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" state x;\n",
|
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" init x;\n",
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"\n",
|
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" trans\n",
|
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" x -> x { guard a < 3 && b < 3; effect a = a + 1; },\n",
|
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" x -> x { guard a < 3 && b < 3; effect b = b + 1; };\n",
|
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"}\n",
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"\n",
|
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"process Q {\n",
|
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" state wait, work;\n",
|
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" init wait;\n",
|
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" trans\n",
|
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" wait -> work { guard b > 1; },\n",
|
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" work -> wait { guard a > 1; };\n",
|
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"}\n",
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"\n",
|
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"system async;"
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]
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},
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{
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"cell_type": "markdown",
|
|
"metadata": {},
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"source": [
|
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"Working with an ltsmin model\n",
|
|
"----------------------------\n",
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"\n",
|
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"Printing an ltsmin model shows some information about the variables it contains and their types, however the `info()` methods provide the data in a map that is easier to work with."
|
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]
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},
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{
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"cell_type": "code",
|
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"ltsmin model with the following variables:\n",
|
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" a: int\n",
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" b: int\n",
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" P: ['x']\n",
|
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" Q: ['wait', 'work']"
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]
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},
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|
"execution_count": 7,
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"metadata": {},
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|
"output_type": "execute_result"
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}
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],
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"source": [
|
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"m"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[('state_size', 4),\n",
|
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" ('types', [('int', []), ('P', ['x']), ('Q', ['wait', 'work'])]),\n",
|
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" ('variables', [('a', 0), ('b', 0), ('P', 1), ('Q', 2)])]"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sorted(m.info().items())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"To obtain a Kripke structure, call `kripke` and supply a list of atomic propositions to observe in the model."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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"text/plain": [
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"k = m.kripke([\"a<1\", \"b>2\"])\n",
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"k"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"<text text-anchor=\"start\" x=\"460.5\" y=\"-217.3\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=0, Q=0</text>\n",
|
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"<text text-anchor=\"start\" x=\"433\" y=\"-202.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
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"</g>\n",
|
|
"<!-- 1->3 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>1->3</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M389.19,-196.93C398.54,-198.28 408.12,-199.66 417.56,-201.02\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"424.75,-202.06 417.37,-204.18 421.29,-201.56 417.82,-201.06 417.82,-201.06 417.82,-201.06 421.29,-201.56 418.27,-197.94 424.75,-202.06 424.75,-202.06\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node6\" class=\"node\">\n",
|
|
"<title>4</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M573,-176.5C573,-176.5 437,-176.5 437,-176.5 431,-176.5 425,-170.5 425,-164.5 425,-164.5 425,-150.5 425,-150.5 425,-144.5 431,-138.5 437,-138.5 437,-138.5 573,-138.5 573,-138.5 579,-138.5 585,-144.5 585,-150.5 585,-150.5 585,-164.5 585,-164.5 585,-170.5 579,-176.5 573,-176.5\"/>\n",
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|
"<text text-anchor=\"start\" x=\"460.5\" y=\"-161.3\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=1, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"433\" y=\"-146.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->4 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>1->4</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M389.19,-174.07C398.54,-172.72 408.12,-171.34 417.56,-169.98\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"424.75,-168.94 418.27,-173.06 421.29,-169.44 417.82,-169.94 417.82,-169.94 417.82,-169.94 421.29,-169.44 417.37,-166.82 424.75,-168.94 424.75,-168.94\"/>\n",
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|
"</g>\n",
|
|
"<!-- 2->4 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>2->4</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M387.23,-140.65C397.28,-142.1 407.62,-143.59 417.8,-145.06\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"424.81,-146.07 417.43,-148.19 421.35,-145.57 417.88,-145.07 417.88,-145.07 417.88,-145.07 421.35,-145.57 418.33,-141.95 424.81,-146.07 424.81,-146.07\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
|
"<title>5</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M571,-120.5C571,-120.5 439,-120.5 439,-120.5 433,-120.5 427,-114.5 427,-108.5 427,-108.5 427,-94.5 427,-94.5 427,-88.5 433,-82.5 439,-82.5 439,-82.5 571,-82.5 571,-82.5 577,-82.5 583,-88.5 583,-94.5 583,-94.5 583,-108.5 583,-108.5 583,-114.5 577,-120.5 571,-120.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"460.5\" y=\"-105.3\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"435\" y=\"-90.3\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->5 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->5</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M387.23,-118.35C397.89,-116.81 408.89,-115.23 419.67,-113.67\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"426.72,-112.65 420.24,-116.77 423.25,-113.15 419.79,-113.65 419.79,-113.65 419.79,-113.65 423.25,-113.15 419.34,-110.54 426.72,-112.65 426.72,-112.65\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 6 -->\n",
|
|
"<g id=\"node8\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M767,-288.5C767,-288.5 635,-288.5 635,-288.5 629,-288.5 623,-282.5 623,-276.5 623,-276.5 623,-262.5 623,-262.5 623,-256.5 629,-250.5 635,-250.5 635,-250.5 767,-250.5 767,-250.5 773,-250.5 779,-256.5 779,-262.5 779,-262.5 779,-276.5 779,-276.5 779,-282.5 773,-288.5 767,-288.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-273.3\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=0, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"631\" y=\"-258.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->6 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>3->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-232.54C589.6,-237.63 608.78,-243.17 626.8,-248.37\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-250.42 626.3,-251.51 630.54,-249.45 627.18,-248.48 627.18,-248.48 627.18,-248.48 630.54,-249.45 628.05,-245.45 633.9,-250.42 633.9,-250.42\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g id=\"node9\" class=\"node\">\n",
|
|
"<title>7</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M769,-232.5C769,-232.5 633,-232.5 633,-232.5 627,-232.5 621,-226.5 621,-220.5 621,-220.5 621,-206.5 621,-206.5 621,-200.5 627,-194.5 633,-194.5 633,-194.5 769,-194.5 769,-194.5 775,-194.5 781,-200.5 781,-206.5 781,-206.5 781,-220.5 781,-220.5 781,-226.5 775,-232.5 769,-232.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-217.3\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=1, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"629\" y=\"-202.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->7 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->7</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M585.19,-213.5C594.54,-213.5 604.12,-213.5 613.56,-213.5\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"620.75,-213.5 613.75,-216.65 617.25,-213.5 613.75,-213.5 613.75,-213.5 613.75,-213.5 617.25,-213.5 613.75,-210.35 620.75,-213.5 620.75,-213.5\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4->7 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>4->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-176.54C589.6,-181.63 608.78,-187.17 626.8,-192.37\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-194.42 626.3,-195.51 630.54,-193.45 627.18,-192.48 627.18,-192.48 627.18,-192.48 630.54,-193.45 628.05,-189.45 633.9,-194.42 633.9,-194.42\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 8 -->\n",
|
|
"<g id=\"node10\" class=\"node\">\n",
|
|
"<title>8</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M769,-176.5C769,-176.5 633,-176.5 633,-176.5 627,-176.5 621,-170.5 621,-164.5 621,-164.5 621,-150.5 621,-150.5 621,-144.5 627,-138.5 633,-138.5 633,-138.5 769,-138.5 769,-138.5 775,-138.5 781,-144.5 781,-150.5 781,-150.5 781,-164.5 781,-164.5 781,-170.5 775,-176.5 769,-176.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-161.3\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"629\" y=\"-146.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->8 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>4->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M585.19,-157.5C594.54,-157.5 604.12,-157.5 613.56,-157.5\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"620.75,-157.5 613.75,-160.65 617.25,-157.5 613.75,-157.5 613.75,-157.5 613.75,-157.5 617.25,-157.5 613.75,-154.35 620.75,-157.5 620.75,-157.5\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 5->8 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-120.54C589.6,-125.63 608.78,-131.17 626.8,-136.37\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-138.42 626.3,-139.51 630.54,-137.45 627.18,-136.48 627.18,-136.48 627.18,-136.48 630.54,-137.45 628.05,-133.45 633.9,-138.42 633.9,-138.42\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 9 -->\n",
|
|
"<g id=\"node11\" class=\"node\">\n",
|
|
"<title>9</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M741.5,-47.5C741.5,-47.5 660.5,-47.5 660.5,-47.5 654.5,-47.5 648.5,-41.5 648.5,-35.5 648.5,-35.5 648.5,-21.5 648.5,-21.5 648.5,-15.5 654.5,-9.5 660.5,-9.5 660.5,-9.5 741.5,-9.5 741.5,-9.5 747.5,-9.5 753.5,-15.5 753.5,-21.5 753.5,-21.5 753.5,-35.5 753.5,-35.5 753.5,-41.5 747.5,-47.5 741.5,-47.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-32.3\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=3, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"696\" y=\"-17.3\" font-family=\"Lato\" font-size=\"14.00\">...</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->9 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>5->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M556.72,-82.42C583.01,-72.52 615.22,-60.4 642.44,-50.16\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"649.24,-47.6 643.8,-53.01 645.97,-48.83 642.69,-50.07 642.69,-50.07 642.69,-50.07 645.97,-48.83 641.58,-47.12 649.24,-47.6 649.24,-47.6\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 10 -->\n",
|
|
"<g id=\"node12\" class=\"node\">\n",
|
|
"<title>10</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M767,-120.5C767,-120.5 635,-120.5 635,-120.5 629,-120.5 623,-114.5 623,-108.5 623,-108.5 623,-94.5 623,-94.5 623,-88.5 629,-82.5 635,-82.5 635,-82.5 767,-82.5 767,-82.5 773,-82.5 779,-88.5 779,-94.5 779,-94.5 779,-108.5 779,-108.5 779,-114.5 773,-120.5 767,-120.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-105.3\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=2, Q=1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"631\" y=\"-90.3\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->10 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>5->10</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M583.23,-101.5C593.89,-101.5 604.89,-101.5 615.67,-101.5\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"622.72,-101.5 615.72,-104.65 619.22,-101.5 615.72,-101.5 615.72,-101.5 615.72,-101.5 619.22,-101.5 615.72,-98.35 622.72,-101.5 622.72,-101.5\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M665.7,-288.54C660.82,-298.03 672.58,-306.5 701,-306.5 721.87,-306.5 733.76,-301.93 736.67,-295.75\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"736.3,-288.54 739.8,-295.37 736.48,-292.03 736.66,-295.53 736.66,-295.53 736.66,-295.53 736.48,-292.03 733.51,-295.69 736.3,-288.54 736.3,-288.54\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 11 -->\n",
|
|
"<g id=\"node13\" class=\"node\">\n",
|
|
"<title>11</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M961,-288.5C961,-288.5 829,-288.5 829,-288.5 823,-288.5 817,-282.5 817,-276.5 817,-276.5 817,-262.5 817,-262.5 817,-256.5 823,-250.5 829,-250.5 829,-250.5 961,-250.5 961,-250.5 967,-250.5 973,-256.5 973,-262.5 973,-262.5 973,-276.5 973,-276.5 973,-282.5 967,-288.5 961,-288.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"850.5\" y=\"-273.3\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=1, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"825\" y=\"-258.3\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->11 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
|
"<title>7->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M767.27,-232.54C784.74,-237.63 803.72,-243.17 821.55,-248.37\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"828.58,-250.42 820.98,-251.48 825.22,-249.44 821.86,-248.46 821.86,-248.46 821.86,-248.46 825.22,-249.44 822.75,-245.44 828.58,-250.42 828.58,-250.42\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 12 -->\n",
|
|
"<g id=\"node14\" class=\"node\">\n",
|
|
"<title>12</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M935.5,-232.5C935.5,-232.5 854.5,-232.5 854.5,-232.5 848.5,-232.5 842.5,-226.5 842.5,-220.5 842.5,-220.5 842.5,-206.5 842.5,-206.5 842.5,-200.5 848.5,-194.5 854.5,-194.5 854.5,-194.5 935.5,-194.5 935.5,-194.5 941.5,-194.5 947.5,-200.5 947.5,-206.5 947.5,-206.5 947.5,-220.5 947.5,-220.5 947.5,-226.5 941.5,-232.5 935.5,-232.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"850.5\" y=\"-217.3\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"890\" y=\"-202.3\" font-family=\"Lato\" font-size=\"14.00\">...</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->12 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>7->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M781.2,-213.5C799.28,-213.5 818.18,-213.5 835.22,-213.5\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"842.41,-213.5 835.41,-216.65 838.91,-213.5 835.41,-213.5 835.41,-213.5 835.41,-213.5 838.91,-213.5 835.41,-210.35 842.41,-213.5 842.41,-213.5\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 8->12 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>8->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M767.27,-176.54C789.34,-182.97 813.84,-190.12 835.36,-196.4\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"842.24,-198.4 834.64,-199.47 838.88,-197.42 835.52,-196.44 835.52,-196.44 835.52,-196.44 838.88,-197.42 836.4,-193.42 842.24,-198.4 842.24,-198.4\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 13 -->\n",
|
|
"<g id=\"node15\" class=\"node\">\n",
|
|
"<title>13</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M935.5,-176.5C935.5,-176.5 854.5,-176.5 854.5,-176.5 848.5,-176.5 842.5,-170.5 842.5,-164.5 842.5,-164.5 842.5,-150.5 842.5,-150.5 842.5,-144.5 848.5,-138.5 854.5,-138.5 854.5,-138.5 935.5,-138.5 935.5,-138.5 941.5,-138.5 947.5,-144.5 947.5,-150.5 947.5,-150.5 947.5,-164.5 947.5,-164.5 947.5,-170.5 941.5,-176.5 935.5,-176.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"850.5\" y=\"-161.3\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=3, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"890\" y=\"-146.3\" font-family=\"Lato\" font-size=\"14.00\">...</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->13 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>8->13</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M781.2,-157.5C799.28,-157.5 818.18,-157.5 835.22,-157.5\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"842.41,-157.5 835.41,-160.65 838.91,-157.5 835.41,-157.5 835.41,-157.5 835.41,-157.5 838.91,-157.5 835.41,-154.35 842.41,-157.5 842.41,-157.5\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 14 -->\n",
|
|
"<g id=\"node16\" class=\"node\">\n",
|
|
"<title>14</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M935.5,-120.5C935.5,-120.5 854.5,-120.5 854.5,-120.5 848.5,-120.5 842.5,-114.5 842.5,-108.5 842.5,-108.5 842.5,-94.5 842.5,-94.5 842.5,-88.5 848.5,-82.5 854.5,-82.5 854.5,-82.5 935.5,-82.5 935.5,-82.5 941.5,-82.5 947.5,-88.5 947.5,-94.5 947.5,-94.5 947.5,-108.5 947.5,-108.5 947.5,-114.5 941.5,-120.5 935.5,-120.5\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"850.5\" y=\"-105.3\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=2, Q=1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"890\" y=\"-90.3\" font-family=\"Lato\" font-size=\"14.00\">...</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->14 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>8->14</title>\n",
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"<!-- 6 -->\n",
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|
"<g id=\"node8\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M767,-280C767,-280 635,-280 635,-280 629,-280 623,-274 623,-268 623,-268 623,-254 623,-254 623,-248 629,-242 635,-242 635,-242 767,-242 767,-242 773,-242 779,-248 779,-254 779,-254 779,-268 779,-268 779,-274 773,-280 767,-280\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-264.8\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=0, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"631\" y=\"-249.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->6 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>3->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-224.04C589.6,-229.13 608.78,-234.67 626.8,-239.87\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-241.92 626.3,-243.01 630.54,-240.95 627.18,-239.98 627.18,-239.98 627.18,-239.98 630.54,-240.95 628.05,-236.95 633.9,-241.92 633.9,-241.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g id=\"node9\" class=\"node\">\n",
|
|
"<title>7</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M769,-224C769,-224 633,-224 633,-224 627,-224 621,-218 621,-212 621,-212 621,-198 621,-198 621,-192 627,-186 633,-186 633,-186 769,-186 769,-186 775,-186 781,-192 781,-198 781,-198 781,-212 781,-212 781,-218 775,-224 769,-224\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=1, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"629\" y=\"-193.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->7 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M585.19,-205C594.54,-205 604.12,-205 613.56,-205\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"620.75,-205 613.75,-208.15 617.25,-205 613.75,-205 613.75,-205 613.75,-205 617.25,-205 613.75,-201.85 620.75,-205 620.75,-205\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 4->7 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>4->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-168.04C589.6,-173.13 608.78,-178.67 626.8,-183.87\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-185.92 626.3,-187.01 630.54,-184.95 627.18,-183.98 627.18,-183.98 627.18,-183.98 630.54,-184.95 628.05,-180.95 633.9,-185.92 633.9,-185.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 8 -->\n",
|
|
"<g id=\"node10\" class=\"node\">\n",
|
|
"<title>8</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M769,-168C769,-168 633,-168 633,-168 627,-168 621,-162 621,-156 621,-156 621,-142 621,-142 621,-136 627,-130 633,-130 633,-130 769,-130 769,-130 775,-130 781,-136 781,-142 781,-142 781,-156 781,-156 781,-162 775,-168 769,-168\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-152.8\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"629\" y=\"-137.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->8 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>4->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M585.19,-149C594.54,-149 604.12,-149 613.56,-149\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"620.75,-149 613.75,-152.15 617.25,-149 613.75,-149 613.75,-149 613.75,-149 617.25,-149 613.75,-145.85 620.75,-149 620.75,-149\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 5->8 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M571.95,-112.04C589.6,-117.13 608.78,-122.67 626.8,-127.87\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"633.9,-129.92 626.3,-131.01 630.54,-128.95 627.18,-127.98 627.18,-127.98 627.18,-127.98 630.54,-128.95 628.05,-124.95 633.9,-129.92 633.9,-129.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 9 -->\n",
|
|
"<g id=\"node11\" class=\"node\">\n",
|
|
"<title>9</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M765,-47C765,-47 637,-47 637,-47 631,-47 625,-41 625,-35 625,-35 625,-21 625,-21 625,-15 631,-9 637,-9 637,-9 765,-9 765,-9 771,-9 777,-15 777,-21 777,-21 777,-35 777,-35 777,-41 771,-47 765,-47\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-31.8\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=3, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"633\" y=\"-16.8\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & "b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->9 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>5->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M562.9,-73.94C585.89,-66.23 612.54,-57.3 636.19,-49.38\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"643.11,-47.06 637.47,-52.27 639.79,-48.17 636.47,-49.29 636.47,-49.29 636.47,-49.29 639.79,-48.17 635.47,-46.3 643.11,-47.06 643.11,-47.06\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 10 -->\n",
|
|
"<g id=\"node12\" class=\"node\">\n",
|
|
"<title>10</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M767,-112C767,-112 635,-112 635,-112 629,-112 623,-106 623,-100 623,-100 623,-86 623,-86 623,-80 629,-74 635,-74 635,-74 767,-74 767,-74 773,-74 779,-80 779,-86 779,-86 779,-100 779,-100 779,-106 773,-112 767,-112\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"656.5\" y=\"-96.8\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=2, Q=1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"631\" y=\"-81.8\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->10 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>5->10</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M583.23,-93C593.89,-93 604.89,-93 615.67,-93\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"622.72,-93 615.72,-96.15 619.22,-93 615.72,-93 615.72,-93 615.72,-93 619.22,-93 615.72,-89.85 622.72,-93 622.72,-93\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>6->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M665.34,-280.04C660.4,-289.53 672.29,-298 701,-298 722.08,-298 734.1,-293.43 737.04,-287.25\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"736.66,-280.04 740.17,-286.87 736.84,-283.53 737.02,-287.03 737.02,-287.03 737.02,-287.03 736.84,-283.53 733.88,-287.19 736.66,-280.04 736.66,-280.04\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 11 -->\n",
|
|
"<g id=\"node13\" class=\"node\">\n",
|
|
"<title>11</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M963,-280C963,-280 831,-280 831,-280 825,-280 819,-274 819,-268 819,-268 819,-254 819,-254 819,-248 825,-242 831,-242 831,-242 963,-242 963,-242 969,-242 975,-248 975,-254 975,-254 975,-268 975,-268 975,-274 969,-280 963,-280\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"852.5\" y=\"-264.8\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=1, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"827\" y=\"-249.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->11 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
|
"<title>7->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M767.95,-224.04C785.6,-229.13 804.78,-234.67 822.8,-239.87\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"829.9,-241.92 822.3,-243.01 826.54,-240.95 823.18,-239.98 823.18,-239.98 823.18,-239.98 826.54,-240.95 824.05,-236.95 829.9,-241.92 829.9,-241.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 12 -->\n",
|
|
"<g id=\"node14\" class=\"node\">\n",
|
|
"<title>12</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M965,-224C965,-224 829,-224 829,-224 823,-224 817,-218 817,-212 817,-212 817,-198 817,-198 817,-192 823,-186 829,-186 829,-186 965,-186 965,-186 971,-186 977,-192 977,-198 977,-198 977,-212 977,-212 977,-218 971,-224 965,-224\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"852.5\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"825\" y=\"-193.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->12 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>7->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M781.19,-205C790.54,-205 800.12,-205 809.56,-205\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"816.75,-205 809.75,-208.15 813.25,-205 809.75,-205 809.75,-205 809.75,-205 813.25,-205 809.75,-201.85 816.75,-205 816.75,-205\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 8->12 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>8->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M767.95,-168.04C785.6,-173.13 804.78,-178.67 822.8,-183.87\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"829.9,-185.92 822.3,-187.01 826.54,-184.95 823.18,-183.98 823.18,-183.98 823.18,-183.98 826.54,-184.95 824.05,-180.95 829.9,-185.92 829.9,-185.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 13 -->\n",
|
|
"<g id=\"node15\" class=\"node\">\n",
|
|
"<title>13</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M963,-168C963,-168 831,-168 831,-168 825,-168 819,-162 819,-156 819,-156 819,-142 819,-142 819,-136 825,-130 831,-130 831,-130 963,-130 963,-130 969,-130 975,-136 975,-142 975,-142 975,-156 975,-156 975,-162 969,-168 963,-168\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"852.5\" y=\"-152.8\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=3, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"827\" y=\"-137.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & "b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->13 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>8->13</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M781.19,-149C791.32,-149 801.72,-149 811.92,-149\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"818.95,-149 811.95,-152.15 815.45,-149 811.95,-149 811.95,-149 811.95,-149 815.45,-149 811.95,-145.85 818.95,-149 818.95,-149\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 14 -->\n",
|
|
"<g id=\"node16\" class=\"node\">\n",
|
|
"<title>14</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M965,-112C965,-112 829,-112 829,-112 823,-112 817,-106 817,-100 817,-100 817,-86 817,-86 817,-80 823,-74 829,-74 829,-74 965,-74 965,-74 971,-74 977,-80 977,-86 977,-86 977,-100 977,-100 977,-106 971,-112 965,-112\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"852.5\" y=\"-96.8\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=2, Q=1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"825\" y=\"-81.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->14 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>8->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M767.95,-129.96C785.6,-124.87 804.78,-119.33 822.8,-114.13\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"829.9,-112.08 824.05,-117.05 826.54,-113.05 823.18,-114.02 823.18,-114.02 823.18,-114.02 826.54,-113.05 822.3,-110.99 829.9,-112.08 829.9,-112.08\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 15 -->\n",
|
|
"<g id=\"node17\" class=\"node\">\n",
|
|
"<title>15</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M959.5,-38C959.5,-38 834.5,-38 834.5,-38 828.5,-38 822.5,-32 822.5,-26 822.5,-26 822.5,-12 822.5,-12 822.5,-6 828.5,0 834.5,0 834.5,0 959.5,0 959.5,0 965.5,0 971.5,-6 971.5,-12 971.5,-12 971.5,-26 971.5,-26 971.5,-32 965.5,-38 959.5,-38\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"852.5\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=3, Q=1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"830.5\" y=\"-7.8\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & "b>2" & dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->15 -->\n",
|
|
"<g id=\"edge21\" class=\"edge\">\n",
|
|
"<title>9->15</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M777.01,-24.52C789.6,-23.94 802.72,-23.33 815.45,-22.74\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"822.47,-22.41 815.62,-25.88 818.97,-22.57 815.48,-22.74 815.48,-22.74 815.48,-22.74 818.97,-22.57 815.33,-19.59 822.47,-22.41 822.47,-22.41\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 10->14 -->\n",
|
|
"<g id=\"edge22\" class=\"edge\">\n",
|
|
"<title>10->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M779.23,-93C789.28,-93 799.62,-93 809.8,-93\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"816.81,-93 809.81,-96.15 813.31,-93 809.81,-93 809.81,-93 809.81,-93 813.31,-93 809.81,-89.85 816.81,-93 816.81,-93\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 10->15 -->\n",
|
|
"<g id=\"edge23\" class=\"edge\">\n",
|
|
"<title>10->15</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M751.96,-73.94C778.67,-63.75 811.66,-51.17 839.33,-40.62\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"845.87,-38.12 840.46,-43.56 842.6,-39.37 839.33,-40.62 839.33,-40.62 839.33,-40.62 842.6,-39.37 838.21,-37.67 845.87,-38.12 845.87,-38.12\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 11->11 -->\n",
|
|
"<g id=\"edge24\" class=\"edge\">\n",
|
|
"<title>11->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M861.34,-280.04C856.4,-289.53 868.29,-298 897,-298 918.08,-298 930.1,-293.43 933.04,-287.25\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"932.66,-280.04 936.17,-286.87 932.84,-283.53 933.02,-287.03 933.02,-287.03 933.02,-287.03 932.84,-283.53 929.88,-287.19 932.66,-280.04 932.66,-280.04\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 16 -->\n",
|
|
"<g id=\"node18\" class=\"node\">\n",
|
|
"<title>16</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1161,-280C1161,-280 1025,-280 1025,-280 1019,-280 1013,-274 1013,-268 1013,-268 1013,-254 1013,-254 1013,-248 1019,-242 1025,-242 1025,-242 1161,-242 1161,-242 1167,-242 1173,-248 1173,-254 1173,-254 1173,-268 1173,-268 1173,-274 1167,-280 1161,-280\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1048.5\" y=\"-264.8\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=2, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1021\" y=\"-249.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 12->16 -->\n",
|
|
"<g id=\"edge25\" class=\"edge\">\n",
|
|
"<title>12->16</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M963.95,-224.04C981.6,-229.13 1000.78,-234.67 1018.8,-239.87\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"1025.9,-241.92 1018.3,-243.01 1022.54,-240.95 1019.18,-239.98 1019.18,-239.98 1019.18,-239.98 1022.54,-240.95 1020.05,-236.95 1025.9,-241.92 1025.9,-241.92\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 17 -->\n",
|
|
"<g id=\"node19\" class=\"node\">\n",
|
|
"<title>17</title>\n",
|
|
"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1159,-168C1159,-168 1027,-168 1027,-168 1021,-168 1015,-162 1015,-156 1015,-156 1015,-142 1015,-142 1015,-136 1021,-130 1027,-130 1027,-130 1159,-130 1159,-130 1165,-130 1171,-136 1171,-142 1171,-142 1171,-156 1171,-156 1171,-162 1165,-168 1159,-168\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1048.5\" y=\"-152.8\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=3, Q=0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1023\" y=\"-137.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & "b>2" & !dead</text>\n",
|
|
"</g>\n",
|
|
"<!-- 12->17 -->\n",
|
|
"<g id=\"edge26\" class=\"edge\">\n",
|
|
"<title>12->17</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M963.95,-185.96C981.6,-180.87 1000.78,-175.33 1018.8,-170.13\"/>\n",
|
|
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"</g>\n",
|
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"<!-- 18 -->\n",
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"<g id=\"node20\" class=\"node\">\n",
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"<title>18</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1161,-224C1161,-224 1025,-224 1025,-224 1019,-224 1013,-218 1013,-212 1013,-212 1013,-198 1013,-198 1013,-192 1019,-186 1025,-186 1025,-186 1161,-186 1161,-186 1167,-186 1173,-192 1173,-198 1173,-198 1173,-212 1173,-212 1173,-218 1167,-224 1161,-224\"/>\n",
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"<text text-anchor=\"start\" x=\"1048.5\" y=\"-208.8\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=2, Q=1</text>\n",
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"<text text-anchor=\"start\" x=\"1021\" y=\"-193.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
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"</g>\n",
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"<!-- 12->18 -->\n",
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"<g id=\"edge27\" class=\"edge\">\n",
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"<title>12->18</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M977.19,-198.35C986.54,-198.24 996.12,-198.22 1005.56,-198.29\"/>\n",
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"</g>\n",
|
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"<!-- 19 -->\n",
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"<g id=\"node21\" class=\"node\">\n",
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"<title>19</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1157,-94C1157,-94 1029,-94 1029,-94 1023,-94 1017,-88 1017,-82 1017,-82 1017,-68 1017,-68 1017,-62 1023,-56 1029,-56 1029,-56 1157,-56 1157,-56 1163,-56 1169,-62 1169,-68 1169,-68 1169,-82 1169,-82 1169,-88 1163,-94 1157,-94\"/>\n",
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"<text text-anchor=\"start\" x=\"1048.5\" y=\"-78.8\" font-family=\"Lato\" font-size=\"14.00\">a=1, b=3, Q=1</text>\n",
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"<text text-anchor=\"start\" x=\"1025\" y=\"-63.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & "b>2" & dead</text>\n",
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"</g>\n",
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"<!-- 13->19 -->\n",
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"<g id=\"edge28\" class=\"edge\">\n",
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"<title>13->19</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M952.93,-129.85C961.02,-126.94 969.24,-123.93 977,-121 997.25,-113.37 1019.35,-104.62 1038.72,-96.83\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1045.44,-94.11 1040.13,-99.65 1042.2,-95.42 1038.95,-96.73 1038.95,-96.73 1038.95,-96.73 1042.2,-95.42 1037.77,-93.81 1045.44,-94.11 1045.44,-94.11\"/>\n",
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|
"</g>\n",
|
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"<!-- 14->18 -->\n",
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"<g id=\"edge29\" class=\"edge\">\n",
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"<title>14->18</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M963.26,-112.07C968.13,-114.69 972.78,-117.66 977,-121 1000.19,-139.37 989.81,-158.63 1013,-177 1015.37,-178.88 1017.88,-180.64 1020.49,-182.29\"/>\n",
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|
"</g>\n",
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"<!-- 14->19 -->\n",
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"<g id=\"edge30\" class=\"edge\">\n",
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"<title>14->19</title>\n",
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|
"<path fill=\"none\" stroke=\"black\" d=\"M977.19,-85.65C987.93,-84.66 998.98,-83.63 1009.77,-82.63\"/>\n",
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|
"</g>\n",
|
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"<!-- 15->15 -->\n",
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"<g id=\"edge31\" class=\"edge\">\n",
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"<title>15->15</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M861.34,-38.04C856.4,-47.53 868.29,-56 897,-56 918.08,-56 930.1,-51.43 933.04,-45.25\"/>\n",
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|
|
"</g>\n",
|
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"<!-- 20 -->\n",
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"<g id=\"node22\" class=\"node\">\n",
|
|
"<title>20</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1357,-280C1357,-280 1221,-280 1221,-280 1215,-280 1209,-274 1209,-268 1209,-268 1209,-254 1209,-254 1209,-248 1215,-242 1221,-242 1221,-242 1357,-242 1357,-242 1363,-242 1369,-248 1369,-254 1369,-254 1369,-268 1369,-268 1369,-274 1363,-280 1357,-280\"/>\n",
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"<text text-anchor=\"start\" x=\"1244.5\" y=\"-264.8\" font-family=\"Lato\" font-size=\"14.00\">a=3, b=2, Q=1</text>\n",
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"<text text-anchor=\"start\" x=\"1217\" y=\"-249.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & !"b>2" & !dead</text>\n",
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"</g>\n",
|
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"<!-- 16->20 -->\n",
|
|
"<g id=\"edge32\" class=\"edge\">\n",
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"<title>16->20</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1173.19,-254.35C1182.54,-254.24 1192.12,-254.22 1201.56,-254.29\"/>\n",
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|
|
"</g>\n",
|
|
"<!-- 21 -->\n",
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|
"<g id=\"node23\" class=\"node\">\n",
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"<title>21</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M1355,-168C1355,-168 1223,-168 1223,-168 1217,-168 1211,-162 1211,-156 1211,-156 1211,-142 1211,-142 1211,-136 1217,-130 1223,-130 1223,-130 1355,-130 1355,-130 1361,-130 1367,-136 1367,-142 1367,-142 1367,-156 1367,-156 1367,-162 1361,-168 1355,-168\"/>\n",
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"<text text-anchor=\"start\" x=\"1244.5\" y=\"-152.8\" font-family=\"Lato\" font-size=\"14.00\">a=2, b=3, Q=1</text>\n",
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"<text text-anchor=\"start\" x=\"1219\" y=\"-137.8\" font-family=\"Lato\" font-size=\"14.00\">!"a<1" & "b>2" & !dead</text>\n",
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"</g>\n",
|
|
"<!-- 17->21 -->\n",
|
|
"<g id=\"edge33\" class=\"edge\">\n",
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"<title>17->21</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1171.23,-142.38C1181.89,-142.24 1192.89,-142.21 1203.67,-142.3\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1210.72,-142.38 1203.68,-145.45 1207.22,-142.34 1203.72,-142.3 1203.72,-142.3 1203.72,-142.3 1207.22,-142.34 1203.75,-139.15 1210.72,-142.38 1210.72,-142.38\"/>\n",
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|
"</g>\n",
|
|
"<!-- 18->12 -->\n",
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"<g id=\"edge36\" class=\"edge\">\n",
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"<title>18->12</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1012.75,-211.65C1003.4,-211.76 993.82,-211.78 984.38,-211.71\"/>\n",
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|
|
"</g>\n",
|
|
"<!-- 18->20 -->\n",
|
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"<g id=\"edge34\" class=\"edge\">\n",
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"<title>18->20</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1159.95,-224.04C1177.6,-229.13 1196.78,-234.67 1214.8,-239.87\"/>\n",
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|
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"</g>\n",
|
|
"<!-- 18->21 -->\n",
|
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"<g id=\"edge35\" class=\"edge\">\n",
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"<title>18->21</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1159.95,-185.96C1177.6,-180.87 1196.78,-175.33 1214.8,-170.13\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1221.9,-168.08 1216.05,-173.05 1218.54,-169.05 1215.18,-170.02 1215.18,-170.02 1215.18,-170.02 1218.54,-169.05 1214.3,-166.99 1221.9,-168.08 1221.9,-168.08\"/>\n",
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"</g>\n",
|
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"<!-- 19->19 -->\n",
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"<g id=\"edge37\" class=\"edge\">\n",
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"<title>19->19</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1057.34,-94.04C1052.4,-103.53 1064.29,-112 1093,-112 1114.08,-112 1126.1,-107.43 1129.04,-101.25\"/>\n",
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"</g>\n",
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"<!-- 20->16 -->\n",
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"<g id=\"edge38\" class=\"edge\">\n",
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"<title>20->16</title>\n",
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"</g>\n",
|
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"<!-- 21->17 -->\n",
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"<g id=\"edge39\" class=\"edge\">\n",
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"<title>21->17</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1210.72,-155.62C1200.05,-155.76 1189.06,-155.79 1178.28,-155.7\"/>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.jupyter.SVG object>"
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]
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},
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"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"k.show('.<0') # unlimited output"
|
|
]
|
|
},
|
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{
|
|
"cell_type": "markdown",
|
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"metadata": {},
|
|
"source": [
|
|
"If we have an LTL proposition to check, we can convert it into an automaton using `spot.translate()`, and synchronize that automaton with the Kripke structure using `spot.otf_product()`. This `otf_product()` function returns product automaton that builds itself on-the-fly, as needed by whatever algorithm \"consumes\" it (here the display routine). "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
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|
"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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"<!-- Generated by graphviz version 2.43.0 (0)\n",
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" -->\n",
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"<!-- Pages: 1 -->\n",
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"<svg width=\"197pt\" height=\"125pt\"\n",
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" viewBox=\"0.00 0.00 197.00 124.80\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 120.8)\">\n",
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"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-120.8 193,-120.8 193,4 -4,4\"/>\n",
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"<text text-anchor=\"start\" x=\"73\" y=\"-86.6\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
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"<!-- I -->\n",
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"<!-- 1 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
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"<title>1</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"56\" cy=\"-22\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"56\" y=\"-18.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- I->1 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-22C2.79,-22 17.15,-22 30.63,-22\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-22 30.94,-25.15 34.44,-22 30.94,-22 30.94,-22 30.94,-22 34.44,-22 30.94,-18.85 37.94,-22 37.94,-22\"/>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M49.62,-39.04C48.32,-48.86 50.45,-58 56,-58 60.17,-58 62.4,-52.86 62.71,-46.14\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"62.38,-39.04 65.85,-45.88 62.54,-42.53 62.71,-46.03 62.71,-46.03 62.71,-46.03 62.54,-42.53 59.56,-46.18 62.38,-39.04 62.38,-39.04\"/>\n",
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"<text text-anchor=\"start\" x=\"11\" y=\"-61.8\" font-family=\"Lato\" font-size=\"14.00\">"a<1" & !"b>2"</text>\n",
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"</g>\n",
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"<!-- 0 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<title>0</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"167\" cy=\"-22\" rx=\"18\" ry=\"18\"/>\n",
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"<ellipse fill=\"none\" stroke=\"black\" cx=\"167\" cy=\"-22\" rx=\"22\" ry=\"22\"/>\n",
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"<text text-anchor=\"middle\" x=\"167\" y=\"-18.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-25.8\" font-family=\"Lato\" font-size=\"14.00\">"b>2"</text>\n",
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"</g>\n",
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"<!-- 0->0 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M156.93,-41.76C155.22,-52.35 158.58,-62 167,-62 173.45,-62 176.93,-56.34 177.43,-48.94\"/>\n",
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"<text text-anchor=\"middle\" x=\"167\" y=\"-65.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe6bc6bf660> >"
|
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]
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},
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
|
"a = spot.translate('\"a<1\" U \"b>2\"'); a"
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]
|
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},
|
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{
|
|
"cell_type": "code",
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"execution_count": 13,
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|
"metadata": {},
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"outputs": [
|
|
{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!-- Generated by graphviz version 2.43.0 (0)\n",
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" -->\n",
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"<!-- Pages: 1 -->\n",
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"<svg width=\"734pt\" height=\"137pt\"\n",
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" viewBox=\"0.00 0.00 734.00 137.49\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(0.5291005291005292 0.5291005291005292) rotate(0) translate(4 256)\">\n",
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"<text text-anchor=\"start\" x=\"669.5\" y=\"-237.8\" font-family=\"Lato\" font-size=\"14.00\">Inf(</text>\n",
|
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"<text text-anchor=\"start\" x=\"690.5\" y=\"-237.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<text text-anchor=\"start\" x=\"706.5\" y=\"-237.8\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
|
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"<text text-anchor=\"start\" x=\"668.5\" y=\"-223.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
|
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"<!-- I -->\n",
|
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"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
|
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"<title>0</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M153,-189C153,-189 50,-189 50,-189 44,-189 38,-183 38,-177 38,-177 38,-165 38,-165 38,-159 44,-153 50,-153 50,-153 153,-153 153,-153 159,-153 165,-159 165,-165 165,-165 165,-177 165,-177 165,-183 159,-189 153,-189\"/>\n",
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"<text text-anchor=\"start\" x=\"46\" y=\"-167.3\" font-family=\"Lato\" font-size=\"14.00\">a=0, b=0, Q=0 * 1</text>\n",
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"</g>\n",
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"<!-- I->0 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->0</title>\n",
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"</g>\n",
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"</g>\n",
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"<title>6->8</title>\n",
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"</g>\n",
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"<!-- 7->u7 -->\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
|
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"<spot.impl.twa_product; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_product > *' at 0x7fe6bc6afc30> >"
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]
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},
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"execution_count": 13,
|
|
"metadata": {},
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"output_type": "execute_result"
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}
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],
|
|
"source": [
|
|
"spot.otf_product(k, a)"
|
|
]
|
|
},
|
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{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
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|
"source": [
|
|
"If we want to create a `model_check` function that takes a model and formula, we need to get the list of atomic propositions used in the formula using `atomic_prop_collect()`. This returns an `atomic_prop_set`:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
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"metadata": {},
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"outputs": [
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|
{
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|
"data": {
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|
"text/latex": [
|
|
"$\\{\\unicode{x201C}\\mathit{a < 2}\\unicode{x201D}, \\unicode{x201C}\\mathit{b == 1}\\unicode{x201D}\\}$"
|
|
],
|
|
"text/plain": [
|
|
"spot.atomic_prop_set([spot.formula(\"\\\"a < 2\\\"\"), spot.formula(\"\\\"b == 1\\\"\")])"
|
|
]
|
|
},
|
|
"execution_count": 14,
|
|
"metadata": {},
|
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"output_type": "execute_result"
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}
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],
|
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"source": [
|
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"a = spot.atomic_prop_collect(spot.formula('\"a < 2\" W \"b == 1\"')); a"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def model_check(f, m):\n",
|
|
" nf = spot.formula.Not(f)\n",
|
|
" ss = m.kripke(spot.atomic_prop_collect(nf))\n",
|
|
" return spot.otf_product(ss, nf.translate()).is_empty() "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"False"
|
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]
|
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},
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"execution_count": 16,
|
|
"metadata": {},
|
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"output_type": "execute_result"
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}
|
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],
|
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"source": [
|
|
"model_check('\"a<1\" R \"b > 1\"', m)"
|
|
]
|
|
},
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{
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|
"cell_type": "markdown",
|
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"metadata": {},
|
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"source": [
|
|
"Instead of `otf_product(x, y).is_empty()` we prefer to call `!x.intersects(y)`. There is also `x.intersecting_run(y)` that can be used to return a counterexample."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def model_debug(f, m):\n",
|
|
" nf = spot.formula.Not(f)\n",
|
|
" ss = m.kripke(spot.atomic_prop_collect(nf))\n",
|
|
" return ss.intersecting_run(nf.translate())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Prefix:\n",
|
|
" a=0, b=0, Q=0\n",
|
|
" | \"a<1\" & !\"b > 1\" & !dead\n",
|
|
" a=1, b=0, Q=0\n",
|
|
" | !\"a<1\" & !\"b > 1\" & !dead\n",
|
|
" a=2, b=0, Q=0\n",
|
|
" | !\"a<1\" & !\"b > 1\" & !dead\n",
|
|
"Cycle:\n",
|
|
" a=3, b=0, Q=0\n",
|
|
" | !\"a<1\" & !\"b > 1\" & dead\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"run = model_debug('\"a<1\" R \"b > 1\"', m); print(run)"
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|
]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"This accepting run can be represented as an automaton (the `True` argument requires the state names to be preserved). This can be more readable."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe6bc6cbcc0> >"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"run.as_twa(True)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"# Saving Kripke structures to some file\n",
|
|
"\n",
|
|
"For experiments, it is sometime useful to save a Kripke structure in the HOA format. The HOA printer will automatically use `state-labels` for Kripke structures."
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]
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|
},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [
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|
{
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|
"name": "stdout",
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"output_type": "stream",
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|
"text": [
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|
"HOA: v1\n",
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|
"States: 22\n",
|
|
"Start: 0\n",
|
|
"AP: 3 \"a<1\" \"b>2\" \"dead\"\n",
|
|
"acc-name: all\n",
|
|
"Acceptance: 0 t\n",
|
|
"properties: state-labels explicit-labels state-acc weak\n",
|
|
"--BODY--\n",
|
|
"State: [0&!1&!2] 0 \"a=0, b=0, Q=0\"\n",
|
|
"1 2\n",
|
|
"State: [!0&!1&!2] 1 \"a=1, b=0, Q=0\"\n",
|
|
"3 4\n",
|
|
"State: [0&!1&!2] 2 \"a=0, b=1, Q=0\"\n",
|
|
"4 5\n",
|
|
"State: [!0&!1&!2] 3 \"a=2, b=0, Q=0\"\n",
|
|
"6 7\n",
|
|
"State: [!0&!1&!2] 4 \"a=1, b=1, Q=0\"\n",
|
|
"7 8\n",
|
|
"State: [0&!1&!2] 5 \"a=0, b=2, Q=0\"\n",
|
|
"8 9 10\n",
|
|
"State: [!0&!1&2] 6 \"a=3, b=0, Q=0\"\n",
|
|
"6\n",
|
|
"State: [!0&!1&!2] 7 \"a=2, b=1, Q=0\"\n",
|
|
"11 12\n",
|
|
"State: [!0&!1&!2] 8 \"a=1, b=2, Q=0\"\n",
|
|
"12 13 14\n",
|
|
"State: [0&1&!2] 9 \"a=0, b=3, Q=0\"\n",
|
|
"15\n",
|
|
"State: [0&!1&!2] 10 \"a=0, b=2, Q=1\"\n",
|
|
"14 15\n",
|
|
"State: [!0&!1&2] 11 \"a=3, b=1, Q=0\"\n",
|
|
"11\n",
|
|
"State: [!0&!1&!2] 12 \"a=2, b=2, Q=0\"\n",
|
|
"16 17 18\n",
|
|
"State: [!0&1&!2] 13 \"a=1, b=3, Q=0\"\n",
|
|
"19\n",
|
|
"State: [!0&!1&!2] 14 \"a=1, b=2, Q=1\"\n",
|
|
"18 19\n",
|
|
"State: [0&1&2] 15 \"a=0, b=3, Q=1\"\n",
|
|
"15\n",
|
|
"State: [!0&!1&!2] 16 \"a=3, b=2, Q=0\"\n",
|
|
"20\n",
|
|
"State: [!0&1&!2] 17 \"a=2, b=3, Q=0\"\n",
|
|
"21\n",
|
|
"State: [!0&!1&!2] 18 \"a=2, b=2, Q=1\"\n",
|
|
"20 21 12\n",
|
|
"State: [!0&1&2] 19 \"a=1, b=3, Q=1\"\n",
|
|
"19\n",
|
|
"State: [!0&!1&!2] 20 \"a=3, b=2, Q=1\"\n",
|
|
"16\n",
|
|
"State: [!0&1&!2] 21 \"a=2, b=3, Q=1\"\n",
|
|
"17\n",
|
|
"--END--\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"string = k.to_str('hoa')\n",
|
|
"print(string)"
|
|
]
|
|
},
|
|
{
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|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"You can load this as a Kripke structure by passing the `want_kripke` option to `spot.automaton()`. The type `kripke_graph` stores the Kripke structure explicitly (like a `twa_graph` stores an automaton explicitly), so you may want to avoid it for very large modelsand use it only for development."
|
|
]
|
|
},
|
|
{
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"cell_type": "code",
|
|
"execution_count": 21,
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|
"metadata": {},
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|
"outputs": [
|
|
{
|
|
"name": "stdout",
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|
"output_type": "stream",
|
|
"text": [
|
|
"<class 'spot.impl.kripke_graph'>\n"
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|
]
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},
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{
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"data": {
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"</g>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"</g>\n",
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"</g>\n",
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"<!-- 6 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"</g>\n",
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"<title>3->6</title>\n",
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"</g>\n",
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"<!-- 7 -->\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</a>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
|
|
"<spot.impl.kripke_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::kripke_graph > *' at 0x7fe6bc6c4210> >"
|
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]
|
|
},
|
|
"execution_count": 21,
|
|
"metadata": {},
|
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"output_type": "execute_result"
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|
}
|
|
],
|
|
"source": [
|
|
"k2 = spot.automaton(string, want_kripke=True)\n",
|
|
"print(type(k2))\n",
|
|
"k2"
|
|
]
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|
}
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|
],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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