3034e8fcc3
Work around a recent decision in Jupyter Lab and Notebook to render <svg> is inline <img>, breaking tooltips or text selection. (Rerendering all notebooks was painful.) * NEWS: Mention the change. * python/spot/__init__.py: Add a _repr_html_ method to all classes that had a _repr_svg_. It seems Jupyter will use _repr_html_ by default. * python/spot/jupyter.py: SVG replace the _repr_svg_ method by a _repr_html. * tests/python/_altscc.ipynb, tests/python/_autparserr.ipynb, tests/python/_aux.ipynb, tests/python/_mealy.ipynb, tests/python/_partitioned_relabel.ipynb, tests/python/_product_susp.ipynb, tests/python/_product_weak.ipynb, tests/python/_synthesis.ipynb, tests/python/aliases.ipynb, tests/python/alternation.ipynb, tests/python/atva16-fig2a.ipynb, tests/python/atva16-fig2b.ipynb, tests/python/automata-io.ipynb, tests/python/automata.ipynb, tests/python/cav22-figs.ipynb, tests/python/contains.ipynb, tests/python/decompose.ipynb, tests/python/formulas.ipynb, tests/python/games.ipynb, tests/python/gen.ipynb, tests/python/highlighting.ipynb, tests/python/ltsmin-dve.ipynb, tests/python/ltsmin-pml.ipynb, tests/python/parity.ipynb, tests/python/product.ipynb, tests/python/randaut.ipynb, tests/python/satmin.ipynb, tests/python/stutter-inv.ipynb, tests/python/synthesis.ipynb, tests/python/testingaut.ipynb, tests/python/twagraph-internals.ipynb, tests/python/word.ipynb, tests/python/zlktree.ipynb: Update all notebooks.
1261 lines
67 KiB
Text
1261 lines
67 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()\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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},
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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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"$\\mathsf{G} \\mathsf{F} a_{3} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} b)))$"
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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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{
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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)))\")"
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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": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{3} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b)))$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa3 U G(GFa2 U G(GFa1 U G(GFa0 U XXXb)))\")"
|
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]
|
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},
|
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"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": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"text/latex": [
|
|
"$\\mathsf{G} \\mathsf{F} a_{2} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{1} \\mathbin{\\mathsf{U}} \\mathsf{G} (\\mathsf{G} \\mathsf{F} a_{0} \\mathbin{\\mathsf{U}} \\mathsf{X} \\mathsf{X} \\mathsf{X} b))$"
|
|
],
|
|
"text/plain": [
|
|
"spot.formula(\"GFa2 U G(GFa1 U G(GFa0 U XXXb))\")"
|
|
]
|
|
},
|
|
"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": {},
|
|
"outputs": [
|
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"<g id=\"edge5\" class=\"edge\">\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>6</title>\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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"<!-- 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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"<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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"<g id=\"edge9\" class=\"edge\">\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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"<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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"<title>2->1</title>\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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"<!-- 2->3 -->\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M702.77,-33.54C700.17,-43.91 703.25,-54 712,-54 718.7,-54 722.08,-48.08 722.12,-40.66\"/>\n",
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"<text text-anchor=\"start\" x=\"699\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a | b</text>\n",
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"</g>\n",
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"<!-- 9 -->\n",
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"<g id=\"node9\" class=\"node\">\n",
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"<title>9</title>\n",
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"<text text-anchor=\"middle\" x=\"820\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
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"</g>\n",
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"<!-- 3->9 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>3->9</title>\n",
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"<text text-anchor=\"start\" x=\"748\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"</g>\n",
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"<!-- 9->8 -->\n",
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"<g id=\"edge17\" class=\"edge\">\n",
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"<title>9->8</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M835.38,-27.64C849.89,-37.48 872.84,-53.35 892,-68 897.43,-72.15 903.2,-76.82 908.45,-81.17\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"913.9,-85.73 906.51,-83.66 911.22,-83.49 908.53,-81.24 908.53,-81.24 908.53,-81.24 911.22,-83.49 910.55,-78.83 913.9,-85.73 913.9,-85.73\"/>\n",
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"<text text-anchor=\"start\" x=\"856\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"</g>\n",
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"<!-- 9->9 -->\n",
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"<g id=\"edge18\" class=\"edge\">\n",
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"<title>9->9</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M810.77,-33.54C808.17,-43.91 811.25,-54 820,-54 826.7,-54 830.08,-48.08 830.12,-40.66\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"829.23,-33.54 833.23,-40.1 829.67,-37.01 830.1,-40.49 830.1,-40.49 830.1,-40.49 829.67,-37.01 826.98,-40.88 829.23,-33.54 829.23,-33.54\"/>\n",
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"<text text-anchor=\"start\" x=\"802\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"</g>\n",
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"<!-- 5->2 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>5->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M514.12,-81.82C542.63,-84.85 599.92,-90.94 632.63,-94.41\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"640,-95.19 632.71,-97.59 636.52,-94.82 633.04,-94.45 633.04,-94.45 633.04,-94.45 636.52,-94.82 633.37,-91.32 640,-95.19 640,-95.19\"/>\n",
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"<text text-anchor=\"start\" x=\"532\" y=\"-90.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
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"</g>\n",
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"<!-- 6 -->\n",
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"<g id=\"node11\" class=\"node\">\n",
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"<title>6</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"604\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"604\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\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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"<title>5->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M512.19,-71.12C530.47,-60.42 561.29,-42.4 581.88,-30.35\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"588.18,-26.67 583.73,-32.92 585.16,-28.43 582.14,-30.2 582.14,-30.2 582.14,-30.2 585.16,-28.43 580.55,-27.48 588.18,-26.67 588.18,-26.67\"/>\n",
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"<text text-anchor=\"start\" x=\"532\" y=\"-62.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
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"</g>\n",
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"<!-- 6->3 -->\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>6->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M622.03,-18C639.47,-18 666.74,-18 686.49,-18\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"693.66,-18 686.66,-21.15 690.16,-18 686.66,-18 686.66,-18 686.66,-18 690.16,-18 686.66,-14.85 693.66,-18 693.66,-18\"/>\n",
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"<text text-anchor=\"start\" x=\"640\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
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"</g>\n",
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"<!-- 6->6 -->\n",
|
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"<g id=\"edge13\" class=\"edge\">\n",
|
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"<title>6->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M594.77,-33.54C592.17,-43.91 595.25,-54 604,-54 610.7,-54 614.08,-48.08 614.12,-40.66\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"613.23,-33.54 617.23,-40.1 613.67,-37.01 614.1,-40.49 614.1,-40.49 614.1,-40.49 613.67,-37.01 610.98,-40.88 613.23,-33.54 613.23,-33.54\"/>\n",
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"<text text-anchor=\"start\" x=\"586\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</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.jupyter.SVG object>"
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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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}
|
|
],
|
|
"source": [
|
|
"display(sg.aut_pattern(sg.AUT_KS_NCA, 3).show('.a'),\n",
|
|
" sg.aut_pattern(sg.AUT_L_DSA, 3).show('.a'),\n",
|
|
" sg.aut_pattern(sg.AUT_L_NBA, 3).show('.a'))"
|
|
]
|
|
},
|
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{
|
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"cell_type": "markdown",
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"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",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
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"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())"
|
|
]
|
|
}
|
|
],
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"metadata": {
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"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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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.7"
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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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