e7df182a30
* spot/gen/automata.cc, spot/gen/automata.hh, bin/genaut.cc: Rename the enum, function, and command-line option. * tests/core/genaut.test, tests/python/gen.ipynb, tests/python/gen.py: Adjust test cases. * doc/org/genaut.org: Adjust doc.
919 lines
59 KiB
Text
919 lines
59 KiB
Text
{
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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": "3.5.4"
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},
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"name": ""
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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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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"collapsed": false,
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"input": [
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"import spot\n",
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"import spot.gen as sg\n",
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"spot.setup()\n",
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"from IPython.display import display"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 1
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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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"collapsed": false,
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"input": [
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"sg.ltl_pattern(sg.LTL_AND_GF, 3)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"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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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 2,
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"text": [
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"GFp1 & GFp2 & GFp3"
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]
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}
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],
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"prompt_number": 2
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"sg.ltl_pattern(sg.LTL_CCJ_BETA_PRIME, 4)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"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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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 3,
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"text": [
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"F(p & Xp & XXp & XXXp) & F(q & Xq & XXq & XXXq)"
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]
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}
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],
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"prompt_number": 3
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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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"collapsed": false,
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"input": [
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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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"language": "python",
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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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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"(GFp1 | FGp2) & (GFp2 | FGp3) & (GFp3 | FGp4)"
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]
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},
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{
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"latex": [
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"$\\mathsf{F} \\mathsf{G} p_{1}$"
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],
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"metadata": {},
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"output_type": "display_data",
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"text": [
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"FGp1"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"FGp1 & FGp2"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"FGp1 & FGp2 & FGp3"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"p0 U (p1 & Gp2)"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"p0 U (p1 & X(p2 U p3))"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"p0 U (p1 & X(p2 & F(p3 & XF(p4 & XF(p5 & XFp6)))))"
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]
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},
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{
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"latex": [
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"$\\mathsf{F} (p_{0} \\land \\mathsf{X} \\mathsf{G} p_{1})$"
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],
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"metadata": {},
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"output_type": "display_data",
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"text": [
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"F(p0 & XGp1)"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"F(p0 & X(p1 & XFp2))"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"F(p0 & X(p1 U p2))"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"GFp0 | FGp1"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"G(p0 -> (p1 U p2))"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"G(p0 & XF(p1 & XF(p2 & XFp3)))"
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]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"GFp1 & GFp2 & GFp3 & GFp0 & GFp4"
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|
]
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},
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{
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
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"(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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{
|
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"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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"metadata": {},
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"output_type": "display_data",
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"text": [
|
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"G(p0 -> (p1 U (Gp2 | Gp3)))"
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]
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}
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],
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"prompt_number": 4
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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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"# Automata patterns\n",
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"\n",
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"We currently have only a couple of generators of automata:"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"display(sg.aut_pattern(sg.AUT_KS_NCA, 3).show('.a'),\n",
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" sg.aut_pattern(sg.AUT_L_DSA, 3).show('.a'),\n",
|
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" sg.aut_pattern(sg.AUT_L_NBA, 3).show('.a'))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"svg": [
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"<g class=\"edge\" id=\"edge15\"><title>9->8</title>\n",
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"<g class=\"edge\" id=\"edge13\"><title>7->1</title>\n",
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"</g>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge5\"><title>2->2</title>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge6\"><title>2->8</title>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge16\"><title>8->7</title>\n",
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"<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"536\" y=\"-166.8\">a & !b</text>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge7\"><title>3->3</title>\n",
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"<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"704.5\" y=\"-57.8\">a | b</text>\n",
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"</g>\n",
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"<!-- 3->9 -->\n",
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"<g class=\"edge\" id=\"edge8\"><title>3->9</title>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge17\"><title>9->8</title>\n",
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"</g>\n",
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"<g class=\"edge\" id=\"edge18\"><title>9->9</title>\n",
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"<g class=\"edge\" id=\"edge11\"><title>5->6</title>\n",
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"</svg>"
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],
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"text": [
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"<IPython.core.display.SVG object>"
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]
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}
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],
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"prompt_number": 5
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},
|
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{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
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"source": [
|
|
"Multiple automata can be generated using the `aut_patterns()` function, which works similarly to `ltl_patterns()`."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"for aut in sg.aut_patterns(sg.AUT_KS_NCA):\n",
|
|
" print(aut.num_states())"
|
|
],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
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|
"stream": "stdout",
|
|
"text": [
|
|
"3\n",
|
|
"5\n",
|
|
"7\n",
|
|
"9\n",
|
|
"11\n",
|
|
"13\n",
|
|
"15\n",
|
|
"17\n",
|
|
"19\n",
|
|
"21\n"
|
|
]
|
|
}
|
|
],
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|
"prompt_number": 6
|
|
}
|
|
],
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"metadata": {}
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}
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]
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}
|