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.
7018 lines
489 KiB
Text
7018 lines
489 KiB
Text
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"source": [
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"import spot\n",
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"spot.setup()\n",
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"from spot.jupyter import display_inline"
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"This notebook presents functions that can be used to solve the Reactive Synthesis problem using games.\n",
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"If you are not familiar with how Spot represents games, please read the `games` notebook first.\n",
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"\n",
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"In Reactive Synthesis, the goal is to build an electronic circuit that reacts to some input signals by producing some output signals, under some LTL constraints that tie both input and output. Of course the input signals are not controllable, so only job is to decide what output signal to produce.\n",
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"\n",
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"# Reactive synthesis in four steps\n",
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"\n",
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"A strategy/control circuit can be derived more conveniently from an LTL/PSL specification.\n",
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"The process is decomposed in three steps:\n",
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"- Creating the game\n",
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"- Solving the game\n",
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"- Simplifying the winning strategy\n",
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"- Building the circuit from the strategy\n",
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"\n",
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"Each of these steps is parameterized by a structure called `synthesis_info`. This structure stores some additional data needed to pass fine-tuning options or to store statistics.\n",
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"\n",
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"The `ltl_to_game` function takes the LTL specification, and the list of controllable atomic propositions (or output signals). It returns a two-player game, where player 0 plays the input variables (and wants to invalidate the acceptance condition), and player 1 plays the output variables (and wants to satisfy the output condition). The conversion from LTL to parity automata can use one of many algorithms, and can be specified in the `synthesis_info` structure (this works like the `--algo=` option of `ltlsynt`)."
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"game has 29 states and 55 edges\n",
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"</g>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1114.83,-561.66C1120.81,-564.6 1127.86,-567.52 1134.65,-569 1155.5,-573.54 1161.6,-572.46 1182.65,-569 1190.35,-567.73 1198.49,-565.38 1205.8,-562.86\"/>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1110.45,-538.94C1116.84,-531.36 1125.46,-522.3 1134.65,-516 1155.76,-501.53 1183.07,-491.05 1203.04,-484.62\"/>\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>6->23</title>\n",
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"<text text-anchor=\"start\" x=\"896.99\" y=\"-363.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
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"<g id=\"node22\" class=\"node\">\n",
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"<title>24</title>\n",
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"<text text-anchor=\"middle\" x=\"478.33\" y=\"-276.3\" font-family=\"Lato\" font-size=\"14.00\">24</text>\n",
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"</g>\n",
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"<!-- 6->24 -->\n",
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"<g id=\"edge21\" class=\"edge\">\n",
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"<title>6->24</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M844.58,-357.72C829.93,-364.59 807.07,-374.15 785.99,-378 759.46,-382.85 752.23,-379.63 725.32,-378 695.83,-376.22 687.62,-378.51 659.32,-370 597.84,-351.51 531.89,-313.2 499.55,-293.04\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"493.55,-289.26 501.15,-290.32 496.51,-291.13 499.47,-292.99 499.47,-292.99 499.47,-292.99 496.51,-291.13 497.8,-295.66 493.55,-289.26 493.55,-289.26\"/>\n",
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"<!-- 23->1 -->\n",
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"<g id=\"edge45\" class=\"edge\">\n",
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"<title>23->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1018.33,-392.27C1031.87,-394.76 1048.79,-399 1062.65,-406 1068.75,-409.08 1074.74,-413.4 1079.98,-417.77\"/>\n",
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"</g>\n",
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"<g id=\"edge46\" class=\"edge\">\n",
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"<title>23->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M963.87,-388.32C944.43,-387.02 918.4,-383.63 896.99,-375 891.43,-372.76 885.93,-369.48 880.98,-366.02\"/>\n",
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"</g>\n",
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"<g id=\"edge47\" class=\"edge\">\n",
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"<title>24->1</title>\n",
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"</g>\n",
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"<g id=\"edge48\" class=\"edge\">\n",
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"<title>24->9</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M508.61,-280C534.97,-280 573.26,-280 597.98,-280\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"605.19,-280 598.19,-283.15 601.69,-280 598.19,-280 598.19,-280 598.19,-280 601.69,-280 598.19,-276.85 605.19,-280 605.19,-280\"/>\n",
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"</g>\n",
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"<g id=\"edge22\" class=\"edge\">\n",
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"<title>7->20</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M879.02,-100.43C899.37,-98.56 933.86,-95.38 959.46,-93.03\"/>\n",
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"<text text-anchor=\"start\" x=\"914.99\" y=\"-102.8\" font-family=\"Lato\" font-size=\"14.00\">i1</text>\n",
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"<title>25</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"755.65,-180 725.49,-162 755.65,-144 785.82,-162 755.65,-180\"/>\n",
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"<text text-anchor=\"middle\" x=\"755.65\" y=\"-158.3\" font-family=\"Lato\" font-size=\"14.00\">25</text>\n",
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"</g>\n",
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"<!-- 7->25 -->\n",
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"<g id=\"edge23\" class=\"edge\">\n",
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"<title>7->25</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M842.9,-100.28C831.3,-99.87 815.97,-100.84 803.99,-107 801.77,-108.14 784.14,-128.96 771.05,-144.65\"/>\n",
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"</g>\n",
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"<g id=\"edge49\" class=\"edge\">\n",
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"<title>25->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M780.91,-159.05C817.53,-155.5 888.64,-152.15 944.99,-171 999.78,-189.34 1053.07,-233.38 1079.83,-257.86\"/>\n",
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"</g>\n",
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"<g id=\"edge50\" class=\"edge\">\n",
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"<title>25->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M771.46,-153.4C789.08,-143.17 818.65,-126 838.72,-114.35\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"844.87,-110.78 840.4,-117.01 841.85,-112.53 838.82,-114.29 838.82,-114.29 838.82,-114.29 841.85,-112.53 837.24,-111.57 844.87,-110.78 844.87,-110.78\"/>\n",
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"</g>\n",
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"<g id=\"edge24\" class=\"edge\">\n",
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"<title>8->20</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M350.18,-196.1C356.12,-193.66 362.97,-191.03 369.33,-189 575.64,-123.29 627.97,-100.51 842.99,-75 884.97,-70.02 933.72,-77.38 963.8,-83.43\"/>\n",
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"</g>\n",
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"<!-- 8->24 -->\n",
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"<g id=\"edge25\" class=\"edge\">\n",
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"<title>8->24</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M350.12,-210.41C369.26,-219.52 402.38,-235.65 429.99,-251 438.99,-256 448.71,-261.87 457,-267.02\"/>\n",
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"</g>\n",
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"<!-- 8->25 -->\n",
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"<g id=\"edge26\" class=\"edge\">\n",
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"<title>8->25</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M351.33,-201.34C414.75,-195.16 638.25,-173.35 722.34,-165.15\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"729.33,-164.47 722.67,-168.29 725.85,-164.81 722.36,-165.15 722.36,-165.15 722.36,-165.15 725.85,-164.81 722.06,-162.01 729.33,-164.47 729.33,-164.47\"/>\n",
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"</g>\n",
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"<!-- 26 -->\n",
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"</g>\n",
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"<g id=\"edge27\" class=\"edge\">\n",
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"<title>8->26</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M340.29,-219.89C345.92,-233.8 355.57,-253.23 369.33,-266 391.1,-286.2 404.95,-278.05 429.99,-294 440.76,-300.86 451.71,-309.95 460.36,-317.73\"/>\n",
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"</g>\n",
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"<!-- 26->3 -->\n",
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"<g id=\"edge51\" class=\"edge\">\n",
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"<title>26->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M482.58,-349.54C493.36,-396.21 532.43,-532 622.32,-532 622.32,-532 622.32,-532 994.32,-532 1022.32,-532 1053.75,-539.5 1074.52,-545.53\"/>\n",
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"</g>\n",
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"<!-- 26->8 -->\n",
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"<g id=\"edge52\" class=\"edge\">\n",
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"<title>26->8</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M449.03,-334.74C424.96,-333.83 390.94,-328.72 369.33,-309 346.62,-288.28 338.62,-252.55 335.81,-228.36\"/>\n",
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"</g>\n",
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"<g id=\"edge28\" class=\"edge\">\n",
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"<title>9->21</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M641.41,-278.02C647.11,-277.37 653.49,-276.64 659.32,-276 688.64,-272.77 695.99,-272.1 725.32,-269 903.77,-250.17 1117.72,-227.75 1197.72,-219.38\"/>\n",
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"</g>\n",
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"<!-- 9->22 -->\n",
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"<g id=\"edge29\" class=\"edge\">\n",
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"<title>9->22</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M639.16,-271.42C687.75,-243.5 842.05,-156.14 896.99,-141 1019.66,-107.19 1068.56,-178.35 1182.65,-122 1197.88,-114.48 1210.31,-99.67 1218.6,-87.46\"/>\n",
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"</g>\n",
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"<!-- 27 -->\n",
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"<g id=\"node28\" class=\"node\">\n",
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"</g>\n",
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"<!-- 9->27 -->\n",
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"<g id=\"edge30\" class=\"edge\">\n",
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"<title>9->27</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M641.59,-279.83C658.45,-279.9 684.78,-280.63 707.32,-284 714.09,-285.01 721.31,-286.58 728.01,-288.25\"/>\n",
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"</g>\n",
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"<!-- 28 -->\n",
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"<g id=\"node29\" class=\"node\">\n",
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"<title>28</title>\n",
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"</g>\n",
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"<!-- 9->28 -->\n",
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"<g id=\"edge31\" class=\"edge\">\n",
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"<title>9->28</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M639.57,-288.49C645.67,-291.84 652.79,-295.67 659.32,-299 680.39,-309.76 686.54,-310.69 707.32,-322 716.36,-326.92 726.09,-332.78 734.37,-337.94\"/>\n",
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"</g>\n",
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"<!-- 27->1 -->\n",
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"<g id=\"edge53\" class=\"edge\">\n",
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"<title>27->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M783.11,-297.65C833.24,-301.8 944.15,-315.87 1023.65,-362 1047.28,-375.71 1068.85,-398.74 1082.52,-415.27\"/>\n",
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"</g>\n",
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"<g id=\"edge54\" class=\"edge\">\n",
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"<title>27->6</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M772.35,-304.2C790,-313.43 818.77,-328.46 838.5,-338.77\"/>\n",
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"<g id=\"edge55\" class=\"edge\">\n",
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"<title>28->1</title>\n",
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"<g id=\"edge56\" class=\"edge\">\n",
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"<title>28->9</title>\n",
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"<title>2->17</title>\n",
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"</g>\n",
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"<g id=\"edge39\" class=\"edge\">\n",
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"<title>17->2</title>\n",
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"<title>3</title>\n",
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"<text text-anchor=\"middle\" x=\"1098.65\" y=\"-549.3\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
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"</g>\n",
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"<g id=\"edge10\" class=\"edge\">\n",
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"<title>3->14</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1114.83,-561.66C1120.81,-564.6 1127.86,-567.52 1134.65,-569 1155.5,-573.54 1161.6,-572.46 1182.65,-569 1190.35,-567.73 1198.49,-565.38 1205.8,-562.86\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1212.8,-560.32 1207.29,-565.67 1209.51,-561.51 1206.22,-562.71 1206.22,-562.71 1206.22,-562.71 1209.51,-561.51 1205.14,-559.75 1212.8,-560.32 1212.8,-560.32\"/>\n",
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"<text text-anchor=\"start\" x=\"1138.65\" y=\"-575.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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"</g>\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<title>3->16</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1110.45,-538.94C1116.84,-531.36 1125.46,-522.3 1134.65,-516 1155.76,-501.53 1183.07,-491.05 1203.04,-484.62\"/>\n",
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"<text text-anchor=\"start\" x=\"1136.65\" y=\"-519.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
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"</g>\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>3->17</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1102.84,-535.43C1109.77,-497.89 1126.28,-412.44 1134.65,-402 1149.45,-383.54 1165.96,-395.77 1182.65,-379 1204.41,-357.13 1217.5,-323.34 1224.23,-301.2\"/>\n",
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"<text text-anchor=\"start\" x=\"1136.65\" y=\"-405.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 18 -->\n",
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"<g id=\"node13\" class=\"node\">\n",
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"<title>18</title>\n",
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"</g>\n",
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"<g id=\"edge13\" class=\"edge\">\n",
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"<title>3->18</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1100.79,-571.08C1103.23,-592.69 1110.86,-628.04 1134.65,-645 1154.19,-658.93 1182.16,-658.05 1202.75,-654.66\"/>\n",
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"<title>18->3</title>\n",
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"</g>\n",
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"<g id=\"node15\" class=\"node\">\n",
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"<title>19</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1444.54,-272 1414.38,-254 1444.54,-236 1474.71,-254 1444.54,-272\"/>\n",
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"<text text-anchor=\"middle\" x=\"1444.54\" y=\"-250.3\" font-family=\"Lato\" font-size=\"14.00\">19</text>\n",
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"</g>\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>4->19</title>\n",
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"</g>\n",
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"<title>20</title>\n",
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"<text text-anchor=\"middle\" x=\"993.32\" y=\"-86.3\" font-family=\"Lato\" font-size=\"14.00\">20</text>\n",
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"</g>\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>4->20</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1318.77,-209.95C1303.93,-204.38 1281.19,-195.95 1261.32,-189 1205.33,-169.43 1190.3,-167.5 1134.65,-147 1093.25,-131.75 1045.84,-112 1018.08,-100.21\"/>\n",
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"</g>\n",
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"<g id=\"edge41\" class=\"edge\">\n",
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"<title>19->4</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1423.96,-248.17C1410.22,-243.96 1391.47,-237.99 1375.21,-232 1370.08,-230.11 1364.63,-227.94 1359.49,-225.82\"/>\n",
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"</g>\n",
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"<!-- 20->5 -->\n",
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"<g id=\"edge42\" class=\"edge\">\n",
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"<title>20->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1010.76,-82.11C1019.77,-77.94 1031.2,-72.89 1041.65,-69 1052.07,-65.12 1063.82,-61.45 1073.85,-58.52\"/>\n",
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"</g>\n",
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"<!-- 21 -->\n",
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"<g id=\"node18\" class=\"node\">\n",
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"<title>21</title>\n",
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"</g>\n",
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"<g id=\"edge16\" class=\"edge\">\n",
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"<title>5->21</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1113.18,-62.89C1130.66,-77.4 1161.34,-104.46 1182.65,-132 1198.2,-152.1 1211.96,-177.91 1220.58,-195.58\"/>\n",
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"</g>\n",
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"<!-- 5->22 -->\n",
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"<g id=\"edge17\" class=\"edge\">\n",
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"<title>5->22</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1116.69,-54.09C1137.38,-56.63 1172.68,-60.97 1198.4,-64.12\"/>\n",
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"</g>\n",
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"<g id=\"edge43\" class=\"edge\">\n",
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"<title>21->4</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1317.73,-216 1310.73,-219.15 1314.23,-216 1310.73,-216 1310.73,-216 1310.73,-216 1314.23,-216 1310.73,-212.85 1317.73,-216 1317.73,-216\"/>\n",
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"</g>\n",
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"<g id=\"edge44\" class=\"edge\">\n",
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"<title>22->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1217.69,-57.44C1208.66,-50.41 1195.73,-41.8 1182.65,-38 1162.16,-32.05 1155.6,-33.97 1134.65,-38 1130.45,-38.81 1126.12,-40.12 1121.99,-41.62\"/>\n",
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"</g>\n",
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"<title>6</title>\n",
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"<text text-anchor=\"middle\" x=\"860.99\" y=\"-346.3\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
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"</g>\n",
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"<g id=\"edge18\" class=\"edge\">\n",
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"<title>6->19</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M878.78,-346.98C917.32,-340.34 1015.16,-325 1097.65,-325 1097.65,-325 1097.65,-325 1336.76,-325 1375.39,-325 1410.7,-292.39 1429.45,-271.37\"/>\n",
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"<text text-anchor=\"start\" x=\"1136.65\" y=\"-328.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 6->20 -->\n",
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"<g id=\"edge19\" class=\"edge\">\n",
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"<title>6->20</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M861.94,-331.87C862.79,-303.42 868.34,-247.92 896.99,-213 911.99,-194.71 928.3,-206.77 944.99,-190 966.75,-168.13 979.84,-134.34 986.57,-112.2\"/>\n",
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"<text text-anchor=\"start\" x=\"900.99\" y=\"-216.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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"</g>\n",
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"<text text-anchor=\"middle\" x=\"993.32\" y=\"-385.3\" font-family=\"Lato\" font-size=\"14.00\">23</text>\n",
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"</g>\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>6->23</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M879,-349.94C896.11,-350.37 923.05,-352.37 944.99,-360 955,-363.48 965.14,-369.32 973.46,-374.86\"/>\n",
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"<text text-anchor=\"start\" x=\"896.99\" y=\"-363.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 6->24 -->\n",
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"<g id=\"edge21\" class=\"edge\">\n",
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"<title>6->24</title>\n",
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"<!-- 23->1 -->\n",
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"<g id=\"edge45\" class=\"edge\">\n",
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"<title>23->1</title>\n",
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"</g>\n",
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"<!-- 7->25 -->\n",
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"</g>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M780.91,-159.05C817.53,-155.5 888.64,-152.15 944.99,-171 999.78,-189.34 1053.07,-233.38 1079.83,-257.86\"/>\n",
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"</g>\n",
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"<g id=\"edge50\" class=\"edge\">\n",
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"<title>25->7</title>\n",
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"</g>\n",
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"<!-- 8->20 -->\n",
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"<g id=\"edge24\" class=\"edge\">\n",
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"<title>8->20</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M350.18,-196.1C356.12,-193.66 362.97,-191.03 369.33,-189 575.64,-123.29 627.97,-100.51 842.99,-75 884.97,-70.02 933.72,-77.38 963.8,-83.43\"/>\n",
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"</g>\n",
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"<!-- 8->24 -->\n",
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"<g id=\"edge25\" class=\"edge\">\n",
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"<title>8->24</title>\n",
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"</g>\n",
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"<g id=\"edge26\" class=\"edge\">\n",
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"<title>8->25</title>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 8->26 -->\n",
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"<g id=\"edge27\" class=\"edge\">\n",
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"<title>8->26</title>\n",
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"<text text-anchor=\"start\" x=\"375.66\" y=\"-297.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 26->3 -->\n",
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"<g id=\"edge51\" class=\"edge\">\n",
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"</g>\n",
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"<!-- 26->8 -->\n",
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"<g id=\"edge52\" class=\"edge\">\n",
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"<title>26->8</title>\n",
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"</g>\n",
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"<g id=\"edge28\" class=\"edge\">\n",
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"</g>\n",
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"<!-- 9->22 -->\n",
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"<g id=\"edge29\" class=\"edge\">\n",
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"<title>9->22</title>\n",
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"</g>\n",
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"<!-- 27 -->\n",
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"</g>\n",
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"<!-- 9->27 -->\n",
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"<g id=\"edge30\" class=\"edge\">\n",
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"</g>\n",
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"<!-- 9->28 -->\n",
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"<g id=\"edge31\" class=\"edge\">\n",
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"<title>9->28</title>\n",
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"</g>\n",
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"<!-- 27->1 -->\n",
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"</g>\n",
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"</g>\n",
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"<!-- 28->1 -->\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 0x7f654cfb32a0> >"
|
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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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],
|
||
"source": [
|
||
"si = spot.synthesis_info()\n",
|
||
"si.s = spot.synthesis_info.algo_LAR # Use LAR algorithm\n",
|
||
"\n",
|
||
"game = spot.ltl_to_game(\"G((F(i0) && F(i1))->(G(i1<->(X(o0)))))\", [\"o0\"], si)\n",
|
||
"print(\"game has\", game.num_states(), \"states and\", game.num_edges(), \"edges\")\n",
|
||
"print(\"output propositions are:\", \", \".join(spot.get_synthesis_output_aps(game)))\n",
|
||
"display(game)"
|
||
]
|
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},
|
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{
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"cell_type": "markdown",
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"id": "4d030586",
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"metadata": {},
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>4->19</title>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>4->20</title>\n",
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"</g>\n",
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"<!-- 19->4 -->\n",
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"<g id=\"edge41\" class=\"edge\">\n",
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"<title>19->4</title>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge16\" class=\"edge\">\n",
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"<title>5->21</title>\n",
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"</g>\n",
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"<g id=\"edge17\" class=\"edge\">\n",
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"<title>5->22</title>\n",
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"</g>\n",
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"<!-- 21->4 -->\n",
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"<g id=\"edge43\" class=\"edge\">\n",
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"<title>21->4</title>\n",
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"</g>\n",
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"<g id=\"edge44\" class=\"edge\">\n",
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"<title>22->5</title>\n",
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"</g>\n",
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"<g id=\"edge18\" class=\"edge\">\n",
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"<title>6->19</title>\n",
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"</g>\n",
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"</g>\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>6->23</title>\n",
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"</g>\n",
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"<g id=\"edge21\" class=\"edge\">\n",
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"<title>6->24</title>\n",
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"</g>\n",
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"<!-- 23->1 -->\n",
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"<title>23->1</title>\n",
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"</g>\n",
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"<!-- 23->6 -->\n",
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"<g id=\"edge46\" class=\"edge\">\n",
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"<title>23->6</title>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 24->9 -->\n",
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"<g id=\"edge48\" class=\"edge\">\n",
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"<title>24->9</title>\n",
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"</g>\n",
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"<!-- 7->20 -->\n",
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"<g id=\"edge22\" class=\"edge\">\n",
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"<title>7->20</title>\n",
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"</g>\n",
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"<!-- 7->25 -->\n",
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"<g id=\"edge23\" class=\"edge\">\n",
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"<title>7->25</title>\n",
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"</g>\n",
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"<!-- 25->2 -->\n",
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"<g id=\"edge49\" class=\"edge\">\n",
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"<title>25->2</title>\n",
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"</g>\n",
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"<!-- 25->7 -->\n",
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"<g id=\"edge50\" class=\"edge\">\n",
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"<title>25->7</title>\n",
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"</g>\n",
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"<g id=\"edge24\" class=\"edge\">\n",
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"<title>8->20</title>\n",
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"</g>\n",
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"<!-- 8->24 -->\n",
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"source": [
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"spot.highlight_strategy(game)\n",
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]
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"Once a strategy has been found, it can be extracted as an automaton and simplified using 6 different levels (the default is 2). The output should be interpreted as a Mealy automaton, where transition have the form `(ins)&(outs)` where `ins` and `outs` are Boolean formulas representing possible inputs and outputs (they could be more than just conjunctions of atomic proposition). Mealy machines with this type of labels are called \"separated\" in Spot."
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"simplification lvl 0 : No simplification\n"
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],
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"source": [
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"display_inline(mealy, spot.split_separated_mealy(mealy), per_row=2)"
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]
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},
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"metadata": {},
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"source": [
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"# Converting the separated Mealy machine to AIG\n",
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"\n",
|
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"A separated Mealy machine can be converted to a circuit in the [AIGER format](http://fmv.jku.at/aiger/FORMAT.aiger) using `mealy_machine_to_aig()`. This takes a second argument specifying what type of encoding to use (exactly like `ltlsynt`'s `--aiger=...` option). \n",
|
||
"\n",
|
||
"In this case, the circuit is quite simple: `o0` should be the negation of previous value of `i1`. This is done by storing the value of `i1` in a latch. And the value if `i0` can be ignored."
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]
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},
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"id": "9f344931",
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"text/plain": [
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"<spot.aig; proxy of <Swig Object of type 'std::shared_ptr< spot::aig > *' at 0x7f654cfb21f0> >"
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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": [
|
||
"aig = spot.mealy_machine_to_aig(mealy, \"isop\")\n",
|
||
"display(aig)"
|
||
]
|
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},
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{
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"cell_type": "markdown",
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"id": "92bbe8d0",
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"metadata": {},
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"source": [
|
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"While we are at it, let us mention that you can render those circuits horizontally as follows:"
|
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]
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},
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{
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"id": "3ae7ce32",
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"aig.show('h')"
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"To encode the circuit in the AIGER format (ASCII version) use:"
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]
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},
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"cell_type": "code",
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"metadata": {},
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"text": [
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"aag 3 2 1 1 0\n",
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"2\n",
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"4\n",
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"6 3\n",
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"7\n",
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"i0 i1\n",
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"i1 i0\n",
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"o0 o0\n"
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]
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}
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],
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"source": [
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"print(aig.to_str())"
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]
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},
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"metadata": {},
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"source": [
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"# Adding more inputs and outputs by force"
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]
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},
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"metadata": {},
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"source": [
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"It can happen that propositions declared as output are omitted in the aig circuit (either because they are not part of the specification, or because they do not appear in the winning strategy). In that case those \n",
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"values can take arbitrary values.\n",
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"\n",
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"For instance so following constraint mention `o1` and `i1`, but those atomic proposition are actually unconstrained (`F(... U x)` can be simplified to `Fx`). Without any indication, the circuit built will ignore those variables:"
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]
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},
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"\n",
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"g1 = spot.ltl_to_game(\"G((i0 xor i1) <-> o0)\", [\"o0\"], si)\n",
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"spot.solve_game(g2)\n",
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"spot.highlight_strategy(g2)\n",
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"strat1 = spot.solved_game_to_separated_mealy(g1)\n",
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"strat2 = spot.solved_game_to_separated_mealy(g2)\n",
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"print(\"Reduced strategies:\")\n",
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"display_inline(strat1, strat2)\n",
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"#Method 1\n",
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"print(\"Circuit implementing both machines from a vector of machines:\")\n",
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"aig = spot.mealy_machines_to_aig([strat1, strat2], \"isop\")\n",
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"display(aig)\n",
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"#Method 2\n",
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"strat_comb = spot.mealy_product(strat1, strat2)\n",
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"print(\"Combining the two machines into one.\")\n",
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"display(strat_comb)\n",
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"aig_comb = spot.mealy_machine_to_aig(strat_comb, \"isop\")\n",
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"display(aig_comb)"
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"# Reading an AIGER-file\n",
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"\n",
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"Note that we do not support the full [AIGER syntax](http://fmv.jku.at/aiger/FORMAT.aiger). Our restrictions corresponds to the conventions used in the type of AIGER file we output:\n",
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"- Input variables start at index 2 and are consecutively numbered.\n",
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"- Latch variables start at index (1 + #inputs)×2 and are consecutively numbered.\n",
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"- If some inputs or outputs are named in comments, all of them have to be named.\n",
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}
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],
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