Since we now require Python 3.6, we can use f-strings instead of format() to make the code more readable. * doc/org/tut01.org, doc/org/tut02.org, doc/org/tut03.org, doc/org/tut21.org, doc/org/tut24.org, doc/org/tut90.org, python/spot/__init__.py, python/spot/jupyter.py, tests/python/acc.py, tests/python/acc_cond.ipynb, tests/python/complement_semidet.py, tests/python/decompose.ipynb, tests/python/formulas.ipynb, tests/python/highlighting.ipynb, tests/python/ipnbdoctest.py, tests/python/ltlf.py, tests/python/parity.ipynb, tests/python/product.ipynb, tests/python/relabel.py, tests/python/satmin.ipynb, tests/python/stutter-inv.ipynb, tests/python/twagraph-internals.ipynb, tests/python/zlktree.ipynb: Use f-strings.
6399 lines
444 KiB
Text
6399 lines
444 KiB
Text
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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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"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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"This notebook shows you different ways in which states or transitions can be highlighted in Spot. \n",
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"\n",
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"It should be noted that highlighting works using some special [named properties](https://spot.lrde.epita.fr/concepts.html#named-properties): basically, two maps that are attached to the automaton, and associated state or edge numbers to color numbers. This named properties are fragile: they will be lost if the automaton is transformed into a new automaton, and they can become meaningless of the automaton is modified in place (e.g., if the transitions or states are reordered).\n",
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"\n",
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"Nonetheless, highlighting is OK to use right before displaying or printing the automaton. The `dot` and `hoa` printer both know how to represent highlighted states and transitions.\n",
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"\n",
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"# Manual highlighting"
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]
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},
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"source": [
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"a = spot.translate('a U b U c')"
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]
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},
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"source": [
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"The `#` option of `print_dot()` can be used to display the internal number of each transition "
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"source": [
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"Using these numbers you can selectively highlight some transitions. The second argument is a color number (from a list of predefined colors)."
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"Note that these `highlight_` functions work for edges and states, and come with both singular (changing the color of single state or edge) and plural versions.\n",
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"\n",
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"They modify the automaton in place."
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]
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},
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{
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"cell_type": "code",
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"</g>\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<text text-anchor=\"start\" x=\"174\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\n",
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],
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"text/plain": [
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"<spot.twa; proxy of <Swig Object of type 'std::shared_ptr< spot::twa > *' at 0x7fed16a24420> >"
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]
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},
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"execution_count": 5,
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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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"a.highlight_edge(6, 2).highlight_states((0, 1), 0)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"The plural version can take a list or tuple of state numbers (as above) or of Booleans (as below). In the latter case the indices of the True values give the states to highlight."
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|
]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"</g>\n",
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"<title>2->1</title>\n",
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"</svg>\n"
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],
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"<!-- Pages: 1 -->\n",
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" viewBox=\"0.00 0.00 305.00 148.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"</g>\n",
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"<!-- I->2 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-62C2.79,-62 17.15,-62 30.63,-62\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-62 30.94,-65.15 34.44,-62 30.94,-62 30.94,-62 30.94,-62 34.44,-62 30.94,-58.85 37.94,-62 37.94,-62\"/>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>2->2</title>\n",
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"<path fill=\"none\" stroke=\"#ff7f00\" stroke-width=\"2\" d=\"M49.62,-79.04C48.32,-88.86 50.45,-98 56,-98 60.17,-98 62.4,-92.86 62.71,-86.14\"/>\n",
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"<text text-anchor=\"start\" x=\"38.5\" y=\"-101.8\" font-family=\"Lato\" font-size=\"14.00\">a & !c</text>\n",
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"<!-- 0 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<ellipse fill=\"none\" stroke=\"#1f78b4\" stroke-width=\"2\" cx=\"275\" cy=\"-62\" rx=\"22\" ry=\"22\"/>\n",
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"<text text-anchor=\"middle\" x=\"275\" y=\"-58.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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"</g>\n",
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"<!-- 2->0 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>2->0</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.55,-66.19C101.64,-72.75 160.43,-84.1 210,-78 222.33,-76.48 235.7,-73.38 247.02,-70.3\"/>\n",
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"<text text-anchor=\"start\" x=\"188.5\" y=\"-82.8\" font-family=\"Lato\" font-size=\"14.00\">c</text>\n",
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"</g>\n",
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"<!-- 1 -->\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>1</title>\n",
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"</g>\n",
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"<!-- 2->1 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M73.43,-56.6C97.04,-48.85 140.68,-34.52 167.63,-25.67\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b & !c</text>\n",
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"</g>\n",
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"<!-- 0->0 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M267.32,-82.99C266.37,-93.09 268.93,-102 275,-102 279.55,-102 282.13,-96.99 282.74,-90.22\"/>\n",
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"<text text-anchor=\"start\" x=\"270.5\" y=\"-105.8\" 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=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<path fill=\"none\" stroke=\"#ff4da0\" stroke-width=\"2\" d=\"M208.24,-26.28C219.74,-32.52 235.76,-41.23 249.11,-48.48\"/>\n",
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"<text text-anchor=\"start\" x=\"228\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\">c</text>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<text text-anchor=\"start\" x=\"174\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fed1691bbd0> >"
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]
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},
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"execution_count": 6,
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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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"a.highlight_states([False, True, True], 5)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"# Saving to HOA 1.1\n",
|
|
"\n",
|
|
"When saving to HOA format, the highlighting is only output if version 1.1 of the format is selected, because the headers `spot.highlight.edges` and `spot.highlight.states` contain dots, which are disallowed in version 1. Compare these two outputs:"
|
|
]
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|
},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
|
"HOA: v1\n",
|
|
"States: 3\n",
|
|
"Start: 2\n",
|
|
"AP: 3 \"a\" \"b\" \"c\"\n",
|
|
"acc-name: Buchi\n",
|
|
"Acceptance: 1 Inf(0)\n",
|
|
"properties: trans-labels explicit-labels state-acc deterministic\n",
|
|
"properties: stutter-invariant terminal very-weak\n",
|
|
"--BODY--\n",
|
|
"State: 0 {0}\n",
|
|
"[t] 0\n",
|
|
"State: 1\n",
|
|
"[2] 0\n",
|
|
"[1&!2] 1\n",
|
|
"State: 2\n",
|
|
"[2] 0\n",
|
|
"[!0&1&!2] 1\n",
|
|
"[0&!2] 2\n",
|
|
"--END--\n",
|
|
"\n",
|
|
"HOA: v1.1\n",
|
|
"States: 3\n",
|
|
"Start: 2\n",
|
|
"AP: 3 \"a\" \"b\" \"c\"\n",
|
|
"acc-name: Buchi\n",
|
|
"Acceptance: 1 Inf(0)\n",
|
|
"properties: trans-labels explicit-labels state-acc !complete\n",
|
|
"properties: deterministic stutter-invariant terminal very-weak\n",
|
|
"spot.highlight.states: 0 0 1 5 2 5\n",
|
|
"spot.highlight.edges: 2 1 4 1 5 1 6 2\n",
|
|
"--BODY--\n",
|
|
"State: 0 {0}\n",
|
|
"[t] 0\n",
|
|
"State: 1\n",
|
|
"[2] 0\n",
|
|
"[1&!2] 1\n",
|
|
"State: 2\n",
|
|
"[2] 0\n",
|
|
"[!0&1&!2] 1\n",
|
|
"[0&!2] 2\n",
|
|
"--END--\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(a.to_str('HOA', '1'))\n",
|
|
"print()\n",
|
|
"print(a.to_str('HOA', '1.1'))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
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"metadata": {},
|
|
"source": [
|
|
"# Querying highlights\n",
|
|
"\n",
|
|
"Use `get_highlight_state(s)` or `get_highlight_edge(e)` to retrieve the highlighting color of some state/edge. If no highlighting is present for this state/edge, `None` is returned."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"state 0: 0\n",
|
|
"state 1: 5\n",
|
|
"state 2: 5\n",
|
|
"edge 1: None\n",
|
|
"edge 2: 1\n",
|
|
"edge 3: None\n",
|
|
"edge 4: 1\n",
|
|
"edge 5: 1\n",
|
|
"edge 6: 2\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"for i in range(0, a.num_states()):\n",
|
|
" print(f\"state {i}: {a.get_highlight_state(i)}\")\n",
|
|
"for i in range(1, a.num_edges() + 1):\n",
|
|
" print(f\"edge {i}: {a.get_highlight_edge(i)}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Removing highlights"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Use `None` as the color to remove some specific highlights."
|
|
]
|
|
},
|
|
{
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"cell_type": "code",
|
|
"execution_count": 9,
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"metadata": {},
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"outputs": [
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"</g>\n",
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"<!-- 2->1 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-53.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b & !c</text>\n",
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"</g>\n",
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"<!-- 0->0 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->0</title>\n",
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"</svg>\n"
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" viewBox=\"0.00 0.00 305.00 148.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-144 301,-144 301,4 -4,4\"/>\n",
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"<text text-anchor=\"start\" x=\"127\" y=\"-124.8\" font-family=\"Lato\" font-size=\"14.00\">[Büchi]</text>\n",
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"</g>\n",
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"<!-- I->2 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>I->2</title>\n",
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"</g>\n",
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"<!-- 2->2 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>2->2</title>\n",
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"<path fill=\"none\" stroke=\"#ff7f00\" stroke-width=\"2\" d=\"M49.62,-79.04C48.32,-88.86 50.45,-98 56,-98 60.17,-98 62.4,-92.86 62.71,-86.14\"/>\n",
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"<!-- 1 -->\n",
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"<g id=\"node4\" class=\"node\">\n",
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"<title>1</title>\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<!-- 0->0 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->0</title>\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>1->0</title>\n",
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"<text text-anchor=\"start\" x=\"228\" y=\"-43.8\" font-family=\"Lato\" font-size=\"14.00\">c</text>\n",
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"</g>\n",
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"<!-- 1->1 -->\n",
|
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"<text text-anchor=\"start\" x=\"174\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">b & !c</text>\n",
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],
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"text/plain": [
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"<spot.twa; proxy of <Swig Object of type 'std::shared_ptr< spot::twa > *' at 0x7fed16a248a0> >"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
|
"a.highlight_state(0, None).highlight_edges([4, 2], None)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
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"metadata": {},
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"source": [
|
|
"Or use `remove_highlight_states()` or `remove_highlight_edges()` to remove all highlights."
|
|
]
|
|
},
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|
{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"# Highlighting a run\n",
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"\n",
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"One use of this highlighting is to highlight a run in an automaton.\n",
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"\n",
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"text/plain": [
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]
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},
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"execution_count": 11,
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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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"b = spot.translate('X (F(Ga <-> b) & GF!b)'); b"
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]
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},
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{
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"cell_type": "code",
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{
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"name": "stdout",
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"text": [
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" 4\n",
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" | 1\n",
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" 1\n",
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"\n"
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]
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}
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],
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"source": [
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]
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},
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{
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"The call of `highlight(5)` on the accepting run `r` modified the original automaton `b`:"
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"source": [
|
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"# Highlighting an accepting run in an automaton with arbitrary acceptance\n",
|
|
"\n",
|
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"This is not as easy as finding accepting runs in (generalized) Büchi automata, so let's have a few example for testing."
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]
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},
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{
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"cell_type": "code",
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"outputs": [
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"56\" cy=\"-192\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"56\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
|
|
"</g>\n",
|
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"<!-- I->0 -->\n",
|
|
"<g id=\"edge1\" class=\"edge\">\n",
|
|
"<title>I->0</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-192C2.79,-192 17.15,-192 30.63,-192\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-192 30.94,-195.15 34.44,-192 30.94,-192 30.94,-192 30.94,-192 34.44,-192 30.94,-188.85 37.94,-192 37.94,-192\"/>\n",
|
|
"</g>\n",
|
|
"<!-- 0->0 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>0->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M49.62,-209.04C48.32,-218.86 50.45,-228 56,-228 60.17,-228 62.4,-222.86 62.71,-216.14\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"62.38,-209.04 65.85,-215.88 62.54,-212.53 62.71,-216.03 62.71,-216.03 62.71,-216.03 62.54,-212.53 59.56,-216.18 62.38,-209.04 62.38,-209.04\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"36\" y=\"-246.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"48\" y=\"-231.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>9</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"162\" cy=\"-368\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"162\" y=\"-364.3\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->9 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M66.05,-207.31C84.61,-238.73 127.04,-310.53 148.33,-346.56\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"152.05,-352.85 145.77,-348.43 149.84,-350.09 148.06,-347.08 148.49,-346.82 148.92,-346.57 150.7,-349.58 151.2,-345.22 152.05,-352.85 152.05,-352.85\"/>\n",
|
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"<text text-anchor=\"start\" x=\"92\" y=\"-318.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
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"<text text-anchor=\"start\" x=\"100\" y=\"-303.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
|
"<title>5</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"272\" cy=\"-192\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"272\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->5 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
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"<title>0->5</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M73.45,-187.45C90.45,-183 117.85,-176.53 142,-174 179,-170.13 221.73,-178.67 247.53,-185.26\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"254.35,-187.06 246.77,-188.32 250.96,-186.17 247.58,-185.28 247.58,-185.28 247.58,-185.28 250.96,-186.17 248.38,-182.23 254.35,-187.06 254.35,-187.06\"/>\n",
|
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"<text text-anchor=\"start\" x=\"144\" y=\"-191.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"146\" y=\"-177.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
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"<text text-anchor=\"start\" x=\"162\" y=\"-177.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->5 -->\n",
|
|
"<g id=\"edge27\" class=\"edge\">\n",
|
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"<title>9->5</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M172.21,-352.99C191.42,-321.69 235.81,-249.35 257.95,-213.27\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"261.82,-206.97 260.84,-214.58 259.98,-209.95 258.15,-212.93 258.15,-212.93 258.15,-212.93 259.98,-209.95 255.47,-211.29 261.82,-206.97 261.82,-206.97\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"200\" y=\"-309.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node5\" class=\"node\">\n",
|
|
"<title>1</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"738\" cy=\"-296\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"738\" y=\"-292.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->1 -->\n",
|
|
"<g id=\"edge28\" class=\"edge\">\n",
|
|
"<title>9->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M179.68,-363.21C200.76,-357.58 238.25,-349 271,-349 271,-349 271,-349 439,-349 542.68,-349 663.55,-317.52 713.53,-303.08\"/>\n",
|
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"720.38,-301.08 714.55,-306.07 717.16,-302.54 713.8,-303.52 713.66,-303.04 713.52,-302.56 716.88,-301.58 712.78,-300.02 720.38,-301.08 720.38,-301.08\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"420\" y=\"-352.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8 -->\n",
|
|
"<g id=\"node6\" class=\"node\">\n",
|
|
"<title>8</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"848\" cy=\"-362\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"848\" y=\"-358.3\" font-family=\"Lato\" font-size=\"14.00\">8</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->8 -->\n",
|
|
"<g id=\"edge26\" class=\"edge\">\n",
|
|
"<title>9->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M168.13,-385.13C179.95,-420.64 212.64,-499 271,-499 271,-499 271,-499 739,-499 795.74,-499 827.27,-425.63 840.11,-386.28\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"842.29,-379.35 843.19,-386.97 841.23,-382.69 840.18,-386.03 840.18,-386.03 840.18,-386.03 841.23,-382.69 837.18,-385.08 842.29,-379.35 842.29,-379.35\"/>\n",
|
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"<text text-anchor=\"start\" x=\"490\" y=\"-517.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"498\" y=\"-502.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->0 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>5->0</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M253.9,-194.81C229.22,-198.53 182.14,-204.35 142,-202 121.42,-200.79 98.18,-197.96 81.21,-195.61\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"73.88,-194.58 81.25,-192.44 77.35,-195.07 80.81,-195.56 80.81,-195.56 80.81,-195.56 77.35,-195.07 80.37,-198.68 73.88,-194.58 73.88,-194.58\"/>\n",
|
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"<text text-anchor=\"start\" x=\"142\" y=\"-220.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
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"<text text-anchor=\"start\" x=\"154\" y=\"-205.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6 -->\n",
|
|
"<g id=\"node8\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"384\" cy=\"-192\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"384\" y=\"-188.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->6 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>5->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M290.19,-192C308.59,-192 337.95,-192 358.71,-192\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"365.93,-192 358.93,-195.15 362.43,-192 358.93,-192 358.93,-192 358.93,-192 362.43,-192 358.93,-188.85 365.93,-192 365.93,-192\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"308\" y=\"-210.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"320\" y=\"-195.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->9 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>1->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M725.33,-309.31C722.81,-312.41 720.23,-315.75 718,-319 708.77,-332.45 711.78,-339.71 700,-351 674.45,-375.47 664.38,-387 629,-387 271,-387 271,-387 271,-387 241.58,-387 208.33,-380.08 186.59,-374.59\"/>\n",
|
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"179.68,-372.79 187.24,-371.51 183.19,-373.19 186.58,-374.07 186.45,-374.55 186.33,-375.04 182.94,-374.16 185.66,-377.6 179.68,-372.79 179.68,-372.79\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"420\" y=\"-405.8\" font-family=\"Lato\" font-size=\"14.00\">a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"430\" y=\"-390.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->8 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>1->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M755.89,-298.14C771.54,-300.78 794.91,-306.41 812,-318 820.63,-323.85 828.15,-332.47 833.98,-340.54\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"838.11,-346.55 831.55,-342.56 836.12,-343.66 834.14,-340.78 834.14,-340.78 834.14,-340.78 836.12,-343.66 836.74,-338.99 838.11,-346.55 838.11,-346.55\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"778\" y=\"-336.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"786\" y=\"-321.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->9 -->\n",
|
|
"<g id=\"edge25\" class=\"edge\">\n",
|
|
"<title>8->9</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M835.97,-375.69C818.02,-396.32 780.29,-433 739,-433 271,-433 271,-433 271,-433 234.59,-433 199.9,-405.55 180.06,-386.33\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"174.87,-381.15 182.05,-383.87 177.35,-383.62 179.83,-386.1 179.83,-386.1 179.83,-386.1 177.35,-383.62 177.6,-388.33 174.87,-381.15 174.87,-381.15\"/>\n",
|
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"<text text-anchor=\"start\" x=\"486\" y=\"-451.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"498\" y=\"-436.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g id=\"node9\" class=\"node\">\n",
|
|
"<title>7</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"956\" cy=\"-284\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"956\" y=\"-280.3\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
|
|
"</g>\n",
|
|
"<!-- 8->7 -->\n",
|
|
"<g id=\"edge24\" class=\"edge\">\n",
|
|
"<title>8->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M862.86,-351.8C881.35,-338.2 914.2,-314.02 935.27,-298.52\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"941.14,-294.2 937.37,-300.89 938.32,-296.27 935.5,-298.35 935.5,-298.35 935.5,-298.35 938.32,-296.27 933.63,-295.81 941.14,-294.2 941.14,-294.2\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"884\" y=\"-337.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
|
"<title>2</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"628\" cy=\"-238\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"628\" y=\"-234.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->8 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->8</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M640.19,-251.32C655.99,-269.48 686.46,-302.13 718,-323 741.41,-338.49 749.19,-339.68 776,-348 791.29,-352.74 808.94,-356.23 822.83,-358.54\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"830.11,-359.7 822.7,-361.71 826.65,-359.15 823.2,-358.6 823.2,-358.6 823.2,-358.6 826.65,-359.15 823.69,-355.49 830.11,-359.7 830.11,-359.7\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"718\" y=\"-360.8\" font-family=\"Lato\" font-size=\"14.00\">!a & !b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"730\" y=\"-345.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M618.77,-253.54C616.17,-263.91 619.25,-274 628,-274 634.7,-274 638.08,-268.08 638.12,-260.66\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"637.23,-253.54 641.23,-260.1 637.67,-257.01 638.1,-260.49 638.1,-260.49 638.1,-260.49 637.67,-257.01 634.98,-260.88 637.23,-253.54 637.23,-253.54\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"612\" y=\"-292.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"620\" y=\"-277.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->6 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>2->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M610.84,-243.5C593.19,-249.19 563.96,-257.7 538,-261 509.78,-264.59 502.08,-265.56 474,-261 449.03,-256.95 440.21,-258.22 420,-243 410.15,-235.58 402.09,-224.55 396.2,-214.65\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"392.65,-208.35 398.83,-212.9 394.37,-211.4 396.09,-214.45 396.09,-214.45 396.09,-214.45 394.37,-211.4 393.35,-216 392.65,-208.35 392.65,-208.35\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"488\" y=\"-281.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"<text text-anchor=\"start\" x=\"490\" y=\"-267.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
|
"<text text-anchor=\"start\" x=\"506\" y=\"-267.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->7 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>2->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M646.07,-240.41C700.2,-248.05 868.17,-271.75 930.98,-280.61\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"938.1,-281.62 930.73,-283.76 934.64,-281.13 931.17,-280.64 931.17,-280.64 931.17,-280.64 934.64,-281.13 931.61,-277.52 938.1,-281.62 938.1,-281.62\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"776\" y=\"-266.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->1 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>6->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M394.85,-177.42C409.52,-156.98 439.15,-120.24 474,-102 521.06,-77.36 545.04,-58.16 592,-83 669.1,-123.79 712.87,-226.01 729.36,-272.42\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"731.68,-279.11 726.41,-273.53 730.53,-275.81 729.38,-272.5 729.38,-272.5 729.38,-272.5 730.53,-275.81 732.36,-271.47 731.68,-279.11 731.68,-279.11\"/>\n",
|
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"<text text-anchor=\"start\" x=\"556\" y=\"-86.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->2 -->\n",
|
|
"<g id=\"edge21\" class=\"edge\">\n",
|
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"<title>6->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M400.37,-199.6C406.37,-202.29 413.39,-205.12 420,-207 454.01,-216.66 555.92,-229.55 602.85,-235.17\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"609.89,-236.01 602.57,-238.31 606.42,-235.6 602.94,-235.18 602.94,-235.18 602.94,-235.18 606.42,-235.6 603.31,-232.05 609.89,-236.01 609.89,-236.01\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"490\" y=\"-243.8\" font-family=\"Lato\" font-size=\"14.00\">a & b</text>\n",
|
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"<text text-anchor=\"start\" x=\"474\" y=\"-229.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
|
|
"<text text-anchor=\"start\" x=\"490\" y=\"-229.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"<text text-anchor=\"start\" x=\"506\" y=\"-229.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"<text text-anchor=\"start\" x=\"522\" y=\"-229.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#33a02c\">❹</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3 -->\n",
|
|
"<g id=\"node10\" class=\"node\">\n",
|
|
"<title>3</title>\n",
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"</g>\n",
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"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M301.56,-98.22C319.38,-92 347.83,-82.07 367.86,-75.08\"/>\n",
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"</g>\n",
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"<!-- 6->8 -->\n",
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"<g id=\"edge13\" class=\"edge\">\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 9->3 -->\n",
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"</g>\n",
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"<!-- 9->5 -->\n",
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"</g>\n",
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"</g>\n",
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|
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"<title>3->4</title>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 4->9 -->\n",
|
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|
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"<title>4->9</title>\n",
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"<!-- 4->7 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
|
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|
"</g>\n",
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|
"<!-- 7->2 -->\n",
|
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>7->2</title>\n",
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]
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},
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{
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fed16a25e00> >"
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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": [
|
|
"def show_accrun(string):\n",
|
|
" aut = spot.automaton(string)\n",
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|
" run = aut.accepting_run()\n",
|
|
" run.highlight(5)\n",
|
|
" display(aut)\n",
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|
"\n",
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|
"show_accrun(\"\"\"\n",
|
|
"HOA: v1 States: 10 Start: 0 AP: 2 \"a\" \"b\" Acceptance: 5 (Inf(1) | (Fin(0)\n",
|
|
"& Inf(4)) | Fin(2)) & Fin(3) properties: trans-labels explicit-labels\n",
|
|
"trans-acc --BODY-- State: 0 [0&1] 9 {3} [!0&!1] 0 {3} [0&!1] 5 {0 1} State:\n",
|
|
"1 [0&!1] 9 {4} [0&1] 8 {3} State: 2 [!0&!1] 8 {0} [!0&1] 6 {2 4} [0&1]\n",
|
|
"2 {3} [!0&1] 7 State: 3 [0&!1] 2 {0 4} [!0&!1] 3 {1 3} [!0&1] 4 {0} State: 4\n",
|
|
"[0&!1] 5 {2} [0&1] 0 [!0&1] 1 {0} State: 5 [!0&!1] 0 {3} [!0&!1] 6 {3} State: 6\n",
|
|
"[0&1] 3 {2} [!0&1] 1 [0&1] 2 {0 1 3 4} State: 7 [0&1] 1 [!0&1] 7 {0 2}\n",
|
|
"State: 8 [!0&1] 7 [!0&!1] 9 {0} State: 9 [0&1] 8 {3} [0&!1] 5 [0&!1]\n",
|
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"1 --END--\n",
|
|
"\"\"\")\n",
|
|
"show_accrun(\"\"\"\n",
|
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"HOA: v1 States: 10 Start: 0 AP: 2 \"a\" \"b\" Acceptance: 6 Fin(5) &\n",
|
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"((Fin(1) & (Inf(3) | Inf(4))) | Fin(0) | Fin(2)) properties: trans-labels\n",
|
|
"explicit-labels trans-acc --BODY-- State: 0 [0&1] 8 {0} [0&!1] 6 {2}\n",
|
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"State: 1 [!0&1] 9 {0 4 5} State: 2 [!0&1] 1 State: 3 [0&!1] 3 {2}\n",
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"[0&1] 4 {3 5} State: 4 [0&1] 7 {5} [0&!1] 9 {2} [!0&1] 0 {0 2} State:\n",
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"5 [!0&1] 1 [!0&1] 3 {2 3} State: 6 [0&!1] 8 {1 2 5} [!0&1] 7 {3} State:\n",
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"7 [0&1] 2 {0} [!0&1] 5 State: 8 [0&!1] 3 {4 5} State: 9 [!0&1] 3 {1 2}\n",
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"[0&1] 1 {4} [0&!1] 5 {2} --END--\"\"\")\n",
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"show_accrun(\"\"\"\n",
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"deterministic complete tool: \"ltl2dstar\" \"0.5.4\" name: \"i G F a G F b\"\n",
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"comment: \"Union{Safra[NBA=2],Safra[NBA=2]}\" acc-name: Rabin 2 Acceptance:\n",
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"4 (Fin(0)&Inf(1))|(Fin(2)&Inf(3)) Start: 0 AP: 2 \"a\" \"b\" --BODY-- State:\n",
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"1 0 3 2 --END--\n",
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"\n",
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"Pretty often, accepting runs are found in a product but we want to display them on one of the original automata. This can be done by projecting the runs on those automata before displaying them."
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"source": [
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"text": [
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"Prefix:\n",
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" 1,0\n",
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" | !a & b\n",
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"Cycle:\n",
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"\n"
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]
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}
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],
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"source": [
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]
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},
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"source": [
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"run.highlight(5)\n",
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"run.project(left).highlight(5)\n",
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"run.project(right, True).highlight(5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"<text text-anchor=\"start\" x=\"453.5\" y=\"-103.8\" 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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"</g>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"567.46,-123.15 570.76,-130.08 567.54,-126.65 567.61,-130.15 567.61,-130.15 567.61,-130.15 567.54,-126.65 564.46,-130.22 567.46,-123.15 567.46,-123.15\"/>\n",
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"<text text-anchor=\"start\" x=\"551.5\" y=\"-144.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 8->7 -->\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>8->7</title>\n",
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"<text text-anchor=\"start\" x=\"511\" y=\"-68.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\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=\"#ffffaa\" stroke=\"black\" d=\"M192,-142C192,-142 169,-142 169,-142 163,-142 157,-136 157,-130 157,-130 157,-118 157,-118 157,-112 163,-106 169,-106 169,-106 192,-106 192,-106 198,-106 204,-112 204,-118 204,-118 204,-130 204,-130 204,-136 198,-142 192,-142\"/>\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=\"M85.18,-145.3C90.98,-143.87 97.22,-142.36 103,-141 118.34,-137.4 135.46,-133.58 149.6,-130.47\"/>\n",
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"<title>3</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M291,-185C291,-185 268,-185 268,-185 262,-185 256,-179 256,-173 256,-173 256,-161 256,-161 256,-155 262,-149 268,-149 268,-149 291,-149 291,-149 297,-149 303,-155 303,-161 303,-161 303,-173 303,-173 303,-179 297,-185 291,-185\"/>\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<g id=\"node6\" class=\"node\">\n",
|
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"<title>4</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M291,-120C291,-120 268,-120 268,-120 262,-120 256,-114 256,-108 256,-108 256,-96 256,-96 256,-90 262,-84 268,-84 268,-84 291,-84 291,-84 297,-84 303,-90 303,-96 303,-96 303,-108 303,-108 303,-114 297,-120 291,-120\"/>\n",
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"<title>2->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M204.33,-109.86C209.91,-107.06 216.01,-104.52 222,-103 230.54,-100.84 240.05,-100.07 248.79,-99.98\"/>\n",
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"<text text-anchor=\"middle\" x=\"230\" y=\"-106.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"<g id=\"node7\" class=\"node\">\n",
|
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"<title>5</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M390,-174C390,-174 367,-174 367,-174 361,-174 355,-168 355,-162 355,-162 355,-150 355,-150 355,-144 361,-138 367,-138 367,-138 390,-138 390,-138 396,-138 402,-144 402,-150 402,-150 402,-162 402,-162 402,-168 396,-174 390,-174\"/>\n",
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"<text text-anchor=\"start\" x=\"363\" y=\"-152.3\" font-family=\"Lato\" font-size=\"14.00\">1 * 0</text>\n",
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"</g>\n",
|
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|
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"<g id=\"edge7\" class=\"edge\">\n",
|
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"<title>3->5</title>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"354.68,-158.59 348.08,-162.51 351.2,-158.98 347.72,-159.38 347.72,-159.38 347.72,-159.38 351.2,-158.98 347.37,-156.25 354.68,-158.59 354.68,-158.59\"/>\n",
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"<text text-anchor=\"start\" x=\"325.5\" y=\"-180.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"</g>\n",
|
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"<!-- 4->5 -->\n",
|
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"<g id=\"edge8\" class=\"edge\">\n",
|
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"<title>4->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M303.49,-114.8C316.9,-122.26 333.94,-131.75 348.3,-139.74\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"354.68,-143.29 347.03,-142.64 351.62,-141.59 348.56,-139.89 348.56,-139.89 348.56,-139.89 351.62,-141.59 350.09,-137.14 354.68,-143.29 354.68,-143.29\"/>\n",
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"<text text-anchor=\"start\" x=\"325.5\" y=\"-135.8\" font-family=\"Lato\" font-size=\"14.00\">a</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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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M390,-109C390,-109 367,-109 367,-109 361,-109 355,-103 355,-97 355,-97 355,-85 355,-85 355,-79 361,-73 367,-73 367,-73 390,-73 390,-73 396,-73 402,-79 402,-85 402,-85 402,-97 402,-97 402,-103 396,-109 390,-109\"/>\n",
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"<text text-anchor=\"start\" x=\"363\" y=\"-87.3\" font-family=\"Lato\" font-size=\"14.00\">2 * 0</text>\n",
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"<!-- 4->6 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>4->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M303.03,-95.49C308.84,-94.07 315.11,-92.77 321,-92 329.66,-90.87 339.14,-90.4 347.81,-90.28\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"354.87,-90.24 347.88,-93.43 351.37,-90.26 347.87,-90.28 347.87,-90.28 347.87,-90.28 351.37,-90.26 347.86,-87.13 354.87,-90.24 354.87,-90.24\"/>\n",
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"<text text-anchor=\"middle\" x=\"329\" y=\"-95.8\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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|
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"<g id=\"node9\" class=\"node\">\n",
|
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"<title>7</title>\n",
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"<path fill=\"#ffffaa\" stroke=\"black\" d=\"M571,-123C571,-123 548,-123 548,-123 542,-123 536,-117 536,-111 536,-111 536,-99 536,-99 536,-93 542,-87 548,-87 548,-87 571,-87 571,-87 577,-87 583,-93 583,-99 583,-99 583,-111 583,-111 583,-117 577,-123 571,-123\"/>\n",
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"</g>\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>5->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M402.17,-149.54C434.36,-140.37 493.35,-123.56 528.94,-113.42\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"535.73,-111.49 529.86,-116.43 532.37,-112.45 529,-113.41 529,-113.41 529,-113.41 532.37,-112.45 528.14,-110.38 535.73,-111.49 535.73,-111.49\"/>\n",
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"<text text-anchor=\"start\" x=\"461.5\" y=\"-139.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fed16a27990> >"
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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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"left2 = spot.translate('!b & FG a')\n",
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"right2 = spot.translate('XXXb')\n",
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"prod2 = spot.otf_product(left2, right2) # Note \"otf_product()\"\n",
|
|
"run2 = prod2.accepting_run()\n",
|
|
"run2.project(left2).highlight(5)\n",
|
|
"run2.project(right2, True).highlight(5)\n",
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"print(run2)\n",
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"display(prod2, left2, right2)"
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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": [
|
|
"# Highlighting nondeterminism\n",
|
|
"\n",
|
|
"Sometimes its is hard to locate non-deterministic states inside a large automaton. Here are two functions that can help for that."
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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": 22,
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"metadata": {},
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"outputs": [
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"b = spot.translate('X (F(Ga <-> b) & GF!b)')\n",
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"source": [
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"# Disappearing highlights\n",
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"\n",
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"As explained at the top of this notebook, named properties (such as highlights) are fragile, and you should not really on them being preserved across algorithms. In-place algorithm are probably the worst, because they might modify the automaton and ignore the attached named properties. \n",
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"\n",
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"`randomize()` is one such in-place algorithm: it reorder states or transitions of the automaton. By doing so it renumber the states and edges, and that process would completely invalidate the highlights information. Fortunately `randomize()` know about highlights: it will preserve highlighted states, but it will drop all highlighted edges."
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fed16a27480> >"
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]
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},
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"execution_count": 23,
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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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"spot.randomize(b); b"
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]
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},
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{
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"metadata": {},
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"source": [
|
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"# Highlighting with partial output\n",
|
|
"\n",
|
|
"For simplicity, rendering of partial automata is actually implemented by copying the original automaton and marking some states as \"incomplete\". This also allows the same display code to work with automata generated on-the-fly. However since there is a copy, propagating the highlighting information requires extra work. Let's make sure it has been done:"
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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": 24,
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"metadata": {},
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"outputs": [
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"source": [
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"spot.highlight_nondet_edges(b, 4) # let's get those highlighted edges back\n",
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"display(b, b.show('.<4'), b.show('.<2'))"
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]
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"# Highlighting languages\n",
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|
"\n",
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"For deterministic automata, the function `spot.highlight_languages()` can be used to highlight states that recognize the same language. This can be a great help in reading automata. States with a colored border share their language, and states with a black border all have a language different from all other states."
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]
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"outputs": [
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"<text text-anchor=\"start\" x=\"575\" y=\"-312.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
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"<text text-anchor=\"start\" x=\"571\" y=\"-297.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 7->6 -->\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>7->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M672.72,-235.39C657.52,-234.84 634.78,-233.96 615,-233 611.53,-232.83 607.88,-232.64 604.29,-232.44\"/>\n",
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"<text text-anchor=\"start\" x=\"615\" y=\"-237.8\" font-family=\"Lato\" font-size=\"14.00\">!b & !c</text>\n",
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"</g>\n",
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"<!-- 7->7 -->\n",
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"<g id=\"edge21\" class=\"edge\">\n",
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"<title>7->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M681.43,-251.54C678.73,-261.91 681.92,-272 691,-272 697.95,-272 701.45,-266.08 701.5,-258.66\"/>\n",
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"<text text-anchor=\"start\" x=\"673\" y=\"-275.8\" font-family=\"Lato\" font-size=\"14.00\">!b & c</text>\n",
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"</g>\n",
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"<!-- 1->4 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<text text-anchor=\"start\" x=\"448\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"</g>\n",
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"<!-- 2->4 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
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"<title>2->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M170.32,-224.12C175.52,-237.63 184.9,-255.55 200,-264 288.51,-313.51 416.34,-268.87 467.55,-247.21\"/>\n",
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"</g>\n",
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"<!-- 2->1 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M181.63,-202.23C187.41,-200.7 193.95,-199.12 200,-198 266.82,-185.61 347.05,-180.69 386.56,-178.91\"/>\n",
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"<text text-anchor=\"start\" x=\"278\" y=\"-189.8\" 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=\"edge7\" class=\"edge\">\n",
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"<title>2->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M154.77,-222.54C152.17,-232.91 155.25,-243 164,-243 170.7,-243 174.08,-237.08 174.12,-229.66\"/>\n",
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"<text text-anchor=\"start\" x=\"132\" y=\"-246.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b & !c</text>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>5</title>\n",
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"<text text-anchor=\"middle\" x=\"298\" y=\"-227.3\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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"</g>\n",
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"<!-- 2->5 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>2->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M181.87,-204.49C201.18,-202.22 233.55,-200.3 260,-208 266.05,-209.76 272.09,-212.82 277.48,-216.13\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"283.46,-220.09 275.89,-218.86 280.54,-218.16 277.62,-216.23 277.62,-216.23 277.62,-216.23 280.54,-218.16 279.36,-213.6 283.46,-220.09 283.46,-220.09\"/>\n",
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"<text text-anchor=\"start\" x=\"200\" y=\"-211.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b & c</text>\n",
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"</g>\n",
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"<!-- 5->4 -->\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>5->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M316.29,-231.54C350.38,-232.61 426.36,-235 465.56,-236.23\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"472.89,-236.46 465.79,-239.39 469.39,-236.35 465.89,-236.24 465.89,-236.24 465.89,-236.24 469.39,-236.35 465.99,-233.09 472.89,-236.46 472.89,-236.46\"/>\n",
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"<text text-anchor=\"start\" x=\"408.5\" y=\"-238.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"</g>\n",
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"<!-- 5->1 -->\n",
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"<g id=\"edge13\" class=\"edge\">\n",
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"<title>5->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M313.42,-221.21C320.13,-216.88 328.31,-211.89 336,-208 352.88,-199.46 372.8,-191.59 387.87,-186.05\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"394.84,-183.53 389.33,-188.87 391.55,-184.72 388.26,-185.91 388.26,-185.91 388.26,-185.91 391.55,-184.72 387.19,-182.95 394.84,-183.53 394.84,-183.53\"/>\n",
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"<text text-anchor=\"start\" x=\"336\" y=\"-211.8\" 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=\"edge14\" class=\"edge\">\n",
|
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"<title>5->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M279.88,-231.36C260.26,-231.36 227.3,-230.13 200,-223 195.59,-221.85 191.04,-220.17 186.74,-218.33\"/>\n",
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"<text text-anchor=\"start\" x=\"212\" y=\"-248.8\" font-family=\"Lato\" font-size=\"14.00\">!a & b</text>\n",
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"<text text-anchor=\"start\" x=\"222\" y=\"-233.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"</g>\n",
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"<!-- 3->3 -->\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>3->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M154.77,-49.54C152.17,-59.91 155.25,-70 164,-70 170.7,-70 174.08,-64.08 174.12,-56.66\"/>\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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]
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},
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"execution_count": 25,
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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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"aut = spot.translate('(b W Xa) & GF(c <-> Xb) | a', 'generic', 'det')\n",
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"spot.highlight_languages(aut)\n",
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"aut.show('.bas')"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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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_minor": 2
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}
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