7ee2d9995f
These are meant to test the optimization implemented in issue #568. * spot/gen/automata.hh, spot/gen/automata.cc, bin/genaut.cc: Add support for --cycle-log-nba and --cycle-onehot-nba. * tests/core/genaut.test: Add some tests. * tests/python/gen.ipynb: Illustrate them. * NEWS: Mention them.
3378 lines
220 KiB
Text
3378 lines
220 KiB
Text
{
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"cells": [
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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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"# Formulas & Automata generators\n",
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"\n",
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"The `spot.gen` package contains the functions used to generate the patterns produced by [`genltl`](https://spot.lrde.epita.fr/genltl.html) and [`genaut`](https://spot.lrde.epita.fr/genaut.html)."
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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": 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.gen as sg\n",
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"spot.setup(show_default='.an')\n",
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"from IPython.display import display"
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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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"## LTL patterns\n",
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"\n",
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"Generation of LTL formulas is done via the `ltl_pattern()` function. This takes two arguments: a pattern id, and a pattern size (or index if the id refers to a list)."
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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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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} p_{1} \\land \\mathsf{G} \\mathsf{F} p_{2} \\land \\mathsf{G} \\mathsf{F} p_{3}$"
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],
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"text/plain": [
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"spot.formula(\"GFp1 & GFp2 & GFp3\")"
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]
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},
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"execution_count": 2,
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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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"sg.ltl_pattern(sg.LTL_AND_GF, 3)"
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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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"data": {
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"text/latex": [
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"$\\mathsf{F} (p \\land \\mathsf{X} p \\land \\mathsf{X} \\mathsf{X} p \\land \\mathsf{X} \\mathsf{X} \\mathsf{X} p) \\land \\mathsf{F} (q \\land \\mathsf{X} q \\land \\mathsf{X} \\mathsf{X} q \\land \\mathsf{X} \\mathsf{X} \\mathsf{X} q)$"
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],
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"text/plain": [
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"spot.formula(\"F(p & Xp & XXp & XXXp) & F(q & Xq & XXq & XXXq)\")"
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]
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},
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"execution_count": 3,
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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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"sg.ltl_pattern(sg.LTL_CCJ_BETA_PRIME, 4)"
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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 see the list of supported patterns, the easiest way is to look at the `--help` output of `genltl`. The above pattern for instance is attached to option `--ccj-beta-prime`. The name of the pattern identifier is the same using capital letters, underscores, and an `LTL_` prefix. If a pattern has multiple aliased options in `genltl`, the first one used for the identifier (e.g., `genltl` accept both `--dac-patterns` and `--spec-patterns` as synonyms to denote the patterns of `spot.gen.LTL_DAC_PATTERNS`).\n",
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"\n",
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"Multiple patterns can be generated using the `ltl_patterns()` function. It's arguments should be either can be:\n",
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" - pairs of the form `(id, n)`: in this case the pattern `id` with size/index `n` is returned,\n",
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" - triplets of the form `(id, min, max)`: in this case the patterns are output for all `n` between `min` and `max` included,\n",
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" - an integer `id`: then this is equivalent to `(id, 1, 10)` if the pattern has now upper bound, or `(id, 1, upper)` if the patter `id` has an upper bound `upper`. This is mostly used when the pattern id correspond to a hard-coded list of formulas.\n",
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"\n",
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"Here is an example showing these three types of arguments:"
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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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"scrolled": false
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},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$(\\mathsf{G} \\mathsf{F} p_{1} \\lor \\mathsf{F} \\mathsf{G} p_{2}) \\land (\\mathsf{G} \\mathsf{F} p_{2} \\lor \\mathsf{F} \\mathsf{G} p_{3}) \\land (\\mathsf{G} \\mathsf{F} p_{3} \\lor \\mathsf{F} \\mathsf{G} p_{4})$"
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],
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"text/plain": [
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"spot.formula(\"(GFp1 | FGp2) & (GFp2 | FGp3) & (GFp3 | FGp4)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} \\mathsf{G} p_{1}$"
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],
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"text/plain": [
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"spot.formula(\"FGp1\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} \\mathsf{G} p_{1} \\land \\mathsf{F} \\mathsf{G} p_{2}$"
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],
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"text/plain": [
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"spot.formula(\"FGp1 & FGp2\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} \\mathsf{G} p_{1} \\land \\mathsf{F} \\mathsf{G} p_{2} \\land \\mathsf{F} \\mathsf{G} p_{3}$"
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],
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"text/plain": [
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"spot.formula(\"FGp1 & FGp2 & FGp3\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$p_{0} \\mathbin{\\mathsf{U}} (p_{1} \\land \\mathsf{G} p_{2})$"
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],
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"text/plain": [
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"spot.formula(\"p0 U (p1 & Gp2)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$p_{0} \\mathbin{\\mathsf{U}} (p_{1} \\land \\mathsf{X} (p_{2} \\mathbin{\\mathsf{U}} p_{3}))$"
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],
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"text/plain": [
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"spot.formula(\"p0 U (p1 & X(p2 U p3))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$p_{0} \\mathbin{\\mathsf{U}} (p_{1} \\land \\mathsf{X} (p_{2} \\land \\mathsf{F} (p_{3} \\land \\mathsf{X} \\mathsf{F} (p_{4} \\land \\mathsf{X} \\mathsf{F} (p_{5} \\land \\mathsf{X} \\mathsf{F} p_{6})))))$"
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],
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"text/plain": [
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"spot.formula(\"p0 U (p1 & X(p2 & F(p3 & XF(p4 & XF(p5 & XFp6)))))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} (p_{0} \\land \\mathsf{X} \\mathsf{G} p_{1})$"
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],
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"text/plain": [
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"spot.formula(\"F(p0 & XGp1)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} (p_{0} \\land \\mathsf{X} (p_{1} \\land \\mathsf{X} \\mathsf{F} p_{2}))$"
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],
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"text/plain": [
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"spot.formula(\"F(p0 & X(p1 & XFp2))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{F} (p_{0} \\land \\mathsf{X} (p_{1} \\mathbin{\\mathsf{U}} p_{2}))$"
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],
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"text/plain": [
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"spot.formula(\"F(p0 & X(p1 U p2))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} p_{0} \\lor \\mathsf{F} \\mathsf{G} p_{1}$"
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],
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"text/plain": [
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"spot.formula(\"GFp0 | FGp1\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} (p_{0} \\rightarrow (p_{1} \\mathbin{\\mathsf{U}} p_{2}))$"
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],
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"text/plain": [
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"spot.formula(\"G(p0 -> (p1 U p2))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} (p_{0} \\land \\mathsf{X} \\mathsf{F} (p_{1} \\land \\mathsf{X} \\mathsf{F} (p_{2} \\land \\mathsf{X} \\mathsf{F} p_{3})))$"
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],
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"text/plain": [
|
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"spot.formula(\"G(p0 & XF(p1 & XF(p2 & XFp3)))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} p_{1} \\land \\mathsf{G} \\mathsf{F} p_{2} \\land \\mathsf{G} \\mathsf{F} p_{3} \\land \\mathsf{G} \\mathsf{F} p_{0} \\land \\mathsf{G} \\mathsf{F} p_{4}$"
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],
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"text/plain": [
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"spot.formula(\"GFp1 & GFp2 & GFp3 & GFp0 & GFp4\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$(p_{0} \\mathbin{\\mathsf{U}} (p_{1} \\mathbin{\\mathsf{U}} p_{2})) \\lor (p_{1} \\mathbin{\\mathsf{U}} (p_{2} \\mathbin{\\mathsf{U}} p_{0})) \\lor (p_{2} \\mathbin{\\mathsf{U}} (p_{0} \\mathbin{\\mathsf{U}} p_{1}))$"
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],
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"text/plain": [
|
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"spot.formula(\"(p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
|
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"text/latex": [
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"$\\mathsf{G} (p_{0} \\rightarrow (p_{1} \\mathbin{\\mathsf{U}} (\\mathsf{G} p_{2} \\lor \\mathsf{G} p_{3})))$"
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],
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"text/plain": [
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"spot.formula(\"G(p0 -> (p1 U (Gp2 | Gp3)))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"for f in sg.ltl_patterns((sg.LTL_GH_R, 3), (sg.LTL_AND_FG, 1, 3), sg.LTL_EH_PATTERNS):\n",
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" display(f)"
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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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"Some LTL patterns take two arguments. In this case, the arguments passed to `ltl_pattern()` should be one of:\n",
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"- `(id, n, m)` giving the value of both arguments,\n",
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"- `(id, min1, max1, min2, max2)` specifying a range for both arguments,\n",
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"- `(id, n)` equivalent to `(id, n, n)`,\n",
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"- `id` equivalent to `(id, 1, 3, 1, 3)`."
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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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{
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"data": {
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b)$"
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],
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"text/plain": [
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"spot.formula(\"GFa1 U G(GFa0 U Xb)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
|
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b)$"
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],
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"text/plain": [
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"spot.formula(\"GFa1 U G(GFa0 U XXb)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
|
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b)$"
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],
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"text/plain": [
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"spot.formula(\"GFa1 U G(GFa0 U XXXb)\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
|
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"text/latex": [
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"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b))$"
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],
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"text/plain": [
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"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U Xb))\")"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
|
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"text/latex": [
|
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"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b))$"
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],
|
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"text/plain": [
|
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"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXb))\")"
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]
|
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},
|
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"metadata": {},
|
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"output_type": "display_data"
|
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},
|
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{
|
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"data": {
|
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"text/latex": [
|
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"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b))$"
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],
|
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"text/plain": [
|
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"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXXb))\")"
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]
|
|
},
|
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"metadata": {},
|
|
"output_type": "display_data"
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},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
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"$\\mathsf{G} \\mathsf{F} a_{3} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b)))$"
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],
|
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"text/plain": [
|
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"spot.formula(\"GFa3 U G(GFa2 U G(GFa1 U G(GFa0 U Xb)))\")"
|
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]
|
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},
|
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"metadata": {},
|
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"output_type": "display_data"
|
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},
|
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{
|
|
"data": {
|
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"text/latex": [
|
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"$\\mathsf{G} \\mathsf{F} a_{3} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b)))$"
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],
|
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"text/plain": [
|
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"spot.formula(\"GFa3 U G(GFa2 U G(GFa1 U G(GFa0 U XXb)))\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
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"output_type": "display_data"
|
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},
|
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{
|
|
"data": {
|
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"text/latex": [
|
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"$\\mathsf{G} \\mathsf{F} a_{3} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b)))$"
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],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa3 U G(GFa2 U G(GFa1 U G(GFa0 U XXXb)))\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"for f in sg.ltl_patterns(sg.LTL_SEJK_F):\n",
|
|
" display(f)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {},
|
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"outputs": [
|
|
{
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"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b))$"
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|
],
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|
"text/plain": [
|
|
"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXXb))\")"
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|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b))$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXb))\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b)$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa1 U G(GFa0 U Xb)\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b)$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa1 U G(GFa0 U XXb)\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b))$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U Xb))\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} b))$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXb))\")"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"for f in sg.ltl_patterns((sg.LTL_SEJK_F, 2, 3), (sg.LTL_SEJK_F, 2), (sg.LTL_SEJK_F, 1, 2, 1, 2)):\n",
|
|
" display(f)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Automata patterns\n",
|
|
"\n",
|
|
"We currently have only a couple of generators of automata:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {
|
|
"scrolled": false
|
|
},
|
|
"outputs": [
|
|
{
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|
"data": {
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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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"<!-- Title: ks-nca=3 Pages: 1 -->\n",
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"<svg width=\"729pt\" height=\"310pt\"\n",
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" viewBox=\"0.00 0.00 729.00 309.58\" 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(0.9090909090909091 0.9090909090909091) rotate(0) translate(4 337)\">\n",
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"<text text-anchor=\"start\" x=\"366\" y=\"-302.8\" font-family=\"Lato\" font-size=\"14.00\">[co-Büchi]</text>\n",
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"<!-- I -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->0</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.86,-127 30.86,-130.15 34.36,-127 30.86,-127 30.86,-127 30.86,-127 34.36,-127 30.86,-123.85 37.86,-127 37.86,-127\"/>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<title>1</title>\n",
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"<text text-anchor=\"middle\" x=\"176\" y=\"-240.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 0->1 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M64.32,-148.6C68.75,-170.17 78.67,-202.79 100,-222 113.9,-234.52 134.58,-239.94 150.71,-242.27\"/>\n",
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"<text text-anchor=\"middle\" x=\"120\" y=\"-243.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"345\" cy=\"-188\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"345\" y=\"-184.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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"</g>\n",
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"<!-- 0->2 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M80.65,-134.72C86.78,-136.95 93.62,-139.25 100,-141 179.25,-162.72 275.65,-178.14 319.81,-184.61\"/>\n",
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"<text text-anchor=\"middle\" x=\"176\" y=\"-165.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 3 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>3</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"453\" cy=\"-135\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"453\" y=\"-131.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
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"</g>\n",
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"<!-- 0->3 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>0->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M82.02,-127.43C148.9,-128.8 356.54,-133.05 427.74,-134.5\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"434.97,-134.65 427.91,-137.66 431.47,-134.58 427.97,-134.51 427.97,-134.51 427.97,-134.51 431.47,-134.58 428.04,-131.36 434.97,-134.65 434.97,-134.65\"/>\n",
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"<text text-anchor=\"middle\" x=\"260.5\" y=\"-135.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 4 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
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"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"561\" cy=\"-89\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"561\" y=\"-85.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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"<!-- 0->4 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>0->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M79.73,-116.62C101.81,-105.37 139.95,-89 175,-89 175,-89 175,-89 454,-89 481.99,-89 514.13,-89 535.61,-89\"/>\n",
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"<text text-anchor=\"middle\" x=\"345\" y=\"-92.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"<g id=\"node7\" class=\"node\">\n",
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"<title>5</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"669\" cy=\"-67\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"669\" y=\"-63.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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"</g>\n",
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"<!-- 0->5 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>0->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M73.48,-109.19C92.37,-84.53 130.75,-43 175,-43 175,-43 175,-43 562,-43 591.16,-43 623.74,-51.75 644.98,-58.68\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"651.73,-60.94 644.1,-61.7 648.42,-59.83 645.1,-58.72 645.1,-58.72 645.1,-58.72 648.42,-59.83 646.1,-55.73 651.73,-60.94 651.73,-60.94\"/>\n",
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"<text text-anchor=\"middle\" x=\"399\" y=\"-46.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\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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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"777\" cy=\"-67\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"777\" y=\"-63.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
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"</g>\n",
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"<!-- 0->6 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>0->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M68.37,-106.6C82.8,-70.7 118.41,0 175,0 175,0 175,0 670,0 706.42,0 740.5,-28.61 759.75,-48.43\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"764.78,-53.76 757.68,-50.83 762.38,-51.22 759.97,-48.67 759.97,-48.67 759.97,-48.67 762.38,-51.22 762.27,-46.51 764.78,-53.76 764.78,-53.76\"/>\n",
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"<text text-anchor=\"middle\" x=\"453\" y=\"-3.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 1->0 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M164.93,-229.36C158.53,-220.86 149.66,-210.4 140,-203 124.38,-191.03 114.96,-196.79 100,-184 89.79,-175.27 81.05,-163.27 74.44,-152.53\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"70.81,-146.39 77.08,-150.81 72.59,-149.4 74.37,-152.41 74.37,-152.41 74.37,-152.41 72.59,-149.4 71.66,-154.01 70.81,-146.39 70.81,-146.39\"/>\n",
|
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"<text text-anchor=\"start\" x=\"100\" y=\"-206.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M166.43,-259.54C163.73,-269.91 166.92,-280 176,-280 182.95,-280 186.45,-274.08 186.5,-266.66\"/>\n",
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"<text text-anchor=\"start\" x=\"160\" y=\"-283.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
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"</g>\n",
|
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"<!-- 1->2 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>1->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M186.96,-229.41C193.2,-221.46 201.95,-212.21 212,-207 246.2,-189.28 291.69,-186.57 319.36,-186.84\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"326.67,-186.99 319.6,-189.99 323.17,-186.92 319.67,-186.85 319.67,-186.85 319.67,-186.85 323.17,-186.92 319.73,-183.7 326.67,-186.99 326.67,-186.99\"/>\n",
|
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"<text text-anchor=\"start\" x=\"212\" y=\"-210.8\" font-family=\"Lato\" font-size=\"14.00\">(!a & b) | (a & !b)</text>\n",
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"</g>\n",
|
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"<!-- 2->1 -->\n",
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|
"<g id=\"edge11\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M333.16,-202.02C326.88,-209.14 318.37,-217.26 309,-222 274.51,-239.44 229.1,-243.5 201.53,-244.21\"/>\n",
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"<text text-anchor=\"start\" x=\"242.5\" y=\"-246.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>2->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M335.77,-203.54C333.17,-213.91 336.25,-224 345,-224 351.7,-224 355.08,-218.08 355.12,-210.66\"/>\n",
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"</g>\n",
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"<!-- 2->3 -->\n",
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"<g id=\"edge13\" class=\"edge\">\n",
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"<title>2->3</title>\n",
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"</g>\n",
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"<!-- 3->3 -->\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>3->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M443.77,-150.54C441.17,-160.91 444.25,-171 453,-171 459.7,-171 463.08,-165.08 463.12,-157.66\"/>\n",
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"<text text-anchor=\"start\" x=\"438\" y=\"-174.8\" font-family=\"Lato\" font-size=\"14.00\">!a | b</text>\n",
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"</g>\n",
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"<!-- 3->4 -->\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>3->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M470.1,-128.01C488.1,-120.2 517.38,-107.49 537.61,-98.72\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"544.1,-95.9 538.93,-101.58 540.89,-97.29 537.68,-98.69 537.68,-98.69 537.68,-98.69 540.89,-97.29 536.42,-95.8 544.1,-95.9 544.1,-95.9\"/>\n",
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"<text text-anchor=\"start\" x=\"489\" y=\"-121.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"</g>\n",
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"<!-- 4->4 -->\n",
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"<g id=\"edge16\" class=\"edge\">\n",
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"<title>4->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M551.77,-104.54C549.17,-114.91 552.25,-125 561,-125 567.7,-125 571.08,-119.08 571.12,-111.66\"/>\n",
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"<text text-anchor=\"start\" x=\"546\" y=\"-128.8\" font-family=\"Lato\" font-size=\"14.00\">!a | b</text>\n",
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"</g>\n",
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"<!-- 4->5 -->\n",
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"<g id=\"edge17\" class=\"edge\">\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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},
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{
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>3->4</title>\n",
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"<title>4->4</title>\n",
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"<title>5</title>\n",
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"<text text-anchor=\"middle\" x=\"722\" y=\"-52.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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"</g>\n",
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"<!-- 4->5 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>4->5</title>\n",
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"<title>5->5</title>\n",
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"<title>6</title>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<title>1->1</title>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
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"</g>\n",
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"<!-- 3 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>3</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"554\" cy=\"-56\" rx=\"18\" ry=\"18\"/>\n",
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"<ellipse fill=\"none\" stroke=\"black\" cx=\"554\" cy=\"-56\" rx=\"22\" ry=\"22\"/>\n",
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"</g>\n",
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"<!-- 2->3 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M406.24,-53.32C434.38,-53.83 490.44,-54.86 524.55,-55.48\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"531.89,-55.61 524.83,-58.64 528.39,-55.55 524.89,-55.49 524.89,-55.49 524.89,-55.49 528.39,-55.55 524.94,-52.34 531.89,-55.61 531.89,-55.61\"/>\n",
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"<text text-anchor=\"start\" x=\"424\" y=\"-58.8\" font-family=\"Lato\" font-size=\"14.00\">!p0 & !p1 & p2</text>\n",
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"</g>\n",
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"<!-- 4 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
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"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"747\" cy=\"-57\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"747\" y=\"-53.3\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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"<!-- 3->4 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>3->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M576.17,-56.11C611.96,-56.3 684.18,-56.68 721.87,-56.87\"/>\n",
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"<text text-anchor=\"start\" x=\"594\" y=\"-59.8\" font-family=\"Lato\" font-size=\"14.00\">p0 & !p1 & !p2</text>\n",
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"</g>\n",
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"<!-- 4->4 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>4->4</title>\n",
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"</g>\n",
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"<!-- 4->5 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>4->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M765.26,-56.91C798.66,-56.73 872.21,-56.34 910.6,-56.13\"/>\n",
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"</g>\n",
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"<!-- 5->5 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<!-- 6 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<ellipse fill=\"none\" stroke=\"black\" cx=\"1102\" cy=\"-56\" rx=\"22\" ry=\"22\"/>\n",
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"</g>\n",
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"<!-- 5->6 -->\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<!-- 7 -->\n",
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"<g id=\"node9\" class=\"node\">\n",
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"<title>7</title>\n",
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"<!-- 6->7 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>6->7</title>\n",
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"</g>\n",
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"<!-- 7->7 -->\n",
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"<!-- 8->0 -->\n",
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"</g>\n",
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"<!-- 8->8 -->\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"</svg>\n"
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],
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"text/plain": [
|
|
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fb3eb351680> >"
|
|
]
|
|
},
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"metadata": {},
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"output_type": "display_data"
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|
}
|
|
],
|
|
"source": [
|
|
"examples = []\n",
|
|
"for p in (sg.AUT_KS_NCA, sg.AUT_L_DSA, sg.AUT_L_NBA, sg.AUT_M_NBA,\n",
|
|
" sg.AUT_CYCLIST_PROOF_DBA, sg.AUT_CYCLIST_TRACE_NBA,\n",
|
|
" sg.AUT_CYCLE_LOG_NBA, sg.AUT_CYCLE_ONEHOT_NBA):\n",
|
|
" aut = sg.aut_pattern(p, 3)\n",
|
|
" aut.set_name(sg.aut_pattern_name(p) + \"=3\")\n",
|
|
" examples.append(aut)\n",
|
|
"\n",
|
|
"display(*examples)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Multiple automata can be generated using the `aut_patterns()` function, which works similarly to `ltl_patterns()`."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"3\n",
|
|
"5\n",
|
|
"7\n",
|
|
"9\n",
|
|
"11\n",
|
|
"13\n",
|
|
"15\n",
|
|
"17\n",
|
|
"19\n",
|
|
"21\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"for aut in sg.aut_patterns(sg.AUT_KS_NCA):\n",
|
|
" print(aut.num_states())"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
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"display_name": "Python 3 (ipykernel)",
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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": "3.11.8"
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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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