{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "found-hurricane", "metadata": {}, "outputs": [], "source": [ "import spot\n", "spot.setup()" ] }, { "cell_type": "code", "execution_count": 2, "id": "colonial-testimony", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{0,1,2,3}\n", "\n", "\n", "\n", "1\n", "\n", "{1,2,3}\n", "\n", "\n", "\n", "0->1\n", "\n", "\n", "\n", "\n", "\n", "2\n", "\n", "{0,1,3}\n", "\n", "\n", "\n", "0->2\n", "\n", "\n", "\n", "\n", "\n", "3\n", "\n", "{2,3}\n", "\n", "\n", "\n", "1->3\n", "\n", "\n", "\n", "\n", "\n", "4\n", "\n", "{1,3}\n", "\n", "\n", "\n", "1->4\n", "\n", "\n", "\n", "\n", "\n", "5\n", "\n", "{1,3}\n", "\n", "\n", "\n", "2->5\n", "\n", "\n", "\n", "\n", "\n", "6\n", "\n", "{0,1}\n", "\n", "\n", "\n", "2->6\n", "\n", "\n", "\n", "\n", "\n", "7\n", "\n", "{3}\n", "<7>\n", "\n", "\n", "\n", "3->7\n", "\n", "\n", "\n", "\n", "\n", "8\n", "\n", "{3}\n", "<8>\n", "\n", "\n", "\n", "4->8\n", "\n", "\n", "\n", "\n", "\n", "9\n", "\n", "{1}\n", "<9>\n", "\n", "\n", "\n", "4->9\n", "\n", "\n", "\n", "\n", "\n", "10\n", "\n", "{3}\n", "<10>\n", "\n", "\n", "\n", "5->10\n", "\n", "\n", "\n", "\n", "\n", "11\n", "\n", "{1}\n", "<11>\n", "\n", "\n", "\n", "5->11\n", "\n", "\n", "\n", "\n", "\n", "12\n", "\n", "{1}\n", "<12>\n", "\n", "\n", "\n", "6->12\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(6, 7, False, False, False)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('Fin(0)&Inf(1)&(Inf(2)|Fin(3)) | (Inf(0)|Fin(1))&Fin(2)&Inf(3)')\n", "t = spot.zielonka_tree(c); display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 3, "id": "incorrect-protection", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(7, 3)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(7, [3])" ] }, { "cell_type": "code", "execution_count": 4, "id": "rolled-command", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(7, 2)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(7, [2])" ] }, { "cell_type": "code", "execution_count": 5, "id": "affecting-border", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8, 1)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(7, [1])" ] }, { "cell_type": "code", "execution_count": 6, "id": "accepting-clerk", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(9, 2)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(8, [1])" ] }, { "cell_type": "code", "execution_count": 7, "id": "flexible-country", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(9, 3)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(9, [1])" ] }, { "cell_type": "code", "execution_count": 8, "id": "continental-sessions", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8, 3)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(8, [3])" ] }, { "cell_type": "code", "execution_count": 9, "id": "expired-asian", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10, 0)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(8, [0])" ] }, { "cell_type": "code", "execution_count": 10, "id": "binary-republic", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(7, 0)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(10, [0,2])" ] }, { "cell_type": "code", "execution_count": 11, "id": "starting-liechtenstein", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10, 0)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(7, [0,2])" ] }, { "cell_type": "code", "execution_count": 12, "id": "forced-canyon", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(7, 4)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t.step(7, [])" ] }, { "cell_type": "code", "execution_count": 13, "id": "floppy-chassis", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6, (Fin(0) & Inf(1)) | (Fin(2) & Inf(3)) | (Fin(4) & Inf(5)))\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{0,1,2,3,4,5}\n", "\n", "\n", "\n", "1\n", "\n", "{1,2,3,4,5}\n", "\n", "\n", "\n", "0->1\n", "\n", "\n", "\n", "\n", "\n", "2\n", "\n", "{0,1,3,4,5}\n", "\n", "\n", "\n", "0->2\n", "\n", "\n", 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"8->14\n", "\n", "\n", "\n", "\n", "\n", "15\n", "\n", "{4,5}\n", "\n", "\n", "\n", "9->15\n", "\n", "\n", "\n", "\n", "\n", "16\n", "\n", "{0,1}\n", "\n", "\n", "\n", "10->16\n", "\n", "\n", "\n", "\n", "\n", "17\n", "\n", "{2,3}\n", "\n", "\n", "\n", "11->17\n", "\n", "\n", "\n", "\n", "\n", "18\n", "\n", "{0,1}\n", "\n", "\n", "\n", "12->18\n", "\n", "\n", "\n", "\n", "\n", "19\n", "\n", "{5}\n", "<19>\n", "\n", "\n", "\n", "13->19\n", "\n", "\n", "\n", "\n", "\n", "20\n", "\n", "{3}\n", "<20>\n", "\n", "\n", "\n", "14->20\n", "\n", "\n", "\n", "\n", "\n", "21\n", "\n", "{5}\n", "<21>\n", "\n", "\n", "\n", "15->21\n", "\n", "\n", "\n", "\n", "\n", "22\n", "\n", "{1}\n", "<22>\n", "\n", "\n", "\n", "16->22\n", "\n", "\n", "\n", "\n", "\n", "23\n", "\n", "{3}\n", "<23>\n", "\n", "\n", "\n", "17->23\n", "\n", "\n", "\n", "\n", "\n", "24\n", "\n", "{1}\n", "<24>\n", "\n", "\n", "\n", "18->24\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(6, 19, True, False, False)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('Rabin 3')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 14, "id": "acquired-rogers", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6, (Fin(0) | Inf(1)) & (Fin(2) | Inf(3)) & (Fin(4) | Inf(5)))\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{0,1,2,3,4,5}\n", "\n", "\n", "\n", "1\n", "\n", "{0,2,3,4,5}\n", "\n", "\n", "\n", "0->1\n", "\n", "\n", "\n", "\n", "\n", "2\n", "\n", "{0,1,2,4,5}\n", "\n", "\n", "\n", "0->2\n", "\n", "\n", "\n", "\n", "\n", "3\n", "\n", "{0,1,2,3,4}\n", "\n", "\n", "\n", "0->3\n", "\n", "\n", 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"9->15\n", "\n", "\n", "\n", "\n", "\n", "16\n", "\n", "{0,1}\n", "\n", "\n", "\n", "10->16\n", "\n", "\n", "\n", "\n", "\n", "17\n", "\n", "{2,3}\n", "\n", "\n", "\n", "11->17\n", "\n", "\n", "\n", "\n", "\n", "18\n", "\n", "{0,1}\n", "\n", "\n", "\n", "12->18\n", "\n", "\n", "\n", "\n", "\n", "19\n", "\n", "{4}\n", "<19>\n", "\n", "\n", "\n", "13->19\n", "\n", "\n", "\n", "\n", "\n", "20\n", "\n", "{2}\n", "<20>\n", "\n", "\n", "\n", "14->20\n", "\n", "\n", "\n", "\n", "\n", "21\n", "\n", "{4}\n", "<21>\n", "\n", "\n", "\n", "15->21\n", "\n", "\n", "\n", "\n", "\n", "22\n", "\n", "{0}\n", "<22>\n", "\n", "\n", "\n", "16->22\n", "\n", "\n", "\n", "\n", "\n", "23\n", "\n", "{2}\n", "<23>\n", "\n", "\n", "\n", "17->23\n", "\n", "\n", "\n", "\n", "\n", "24\n", "\n", "{0}\n", "<24>\n", "\n", "\n", "\n", "18->24\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(6, 19, False, True, False)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('Streett 3')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 15, "id": "minimal-douglas", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(5, (Inf(0) & Fin(1)) | (Inf(2) & Fin(3) & Fin(4)))\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{0,1,2,3,4}\n", "\n", "\n", "\n", "1\n", "\n", "{0,2,3,4}\n", "\n", "\n", "\n", "0->1\n", "\n", "\n", "\n", "\n", "\n", "2\n", "\n", "{0,1,2}\n", "\n", "\n", "\n", "0->2\n", "\n", "\n", "\n", "\n", "\n", "3\n", "\n", "{2,3,4}\n", "\n", "\n", "\n", "1->3\n", "\n", "\n", "\n", "\n", "\n", "4\n", "\n", "{0,1}\n", "\n", "\n", "\n", "2->4\n", "\n", "\n", "\n", "\n", "\n", "5\n", "\n", "{2}\n", "<5>\n", "\n", "\n", "\n", "3->5\n", "\n", "\n", "\n", "\n", "\n", "6\n", "\n", "{0}\n", "<6>\n", "\n", "\n", "\n", "4->6\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(2, 5, True, False, False)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('Inf(0)&Fin(1) | (Inf(2)&Fin(3)&Fin(4))')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 16, "id": "tired-thumbnail", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(5, Fin(4) & (Inf(3) | (Fin(2) & (Inf(1) | Fin(0)))))\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{0,1,2,3,4}\n", "\n", "\n", "\n", "1\n", "\n", "{0,1,2,3}\n", "\n", "\n", "\n", "0->1\n", "\n", "\n", "\n", "\n", "\n", "2\n", "\n", "{0,1,2}\n", "\n", "\n", "\n", "1->2\n", "\n", "\n", "\n", "\n", "\n", "3\n", "\n", "{0,1}\n", "\n", "\n", "\n", "2->3\n", "\n", "\n", "\n", "\n", "\n", "4\n", "\n", "{0}\n", "<4>\n", "\n", "\n", "\n", "3->4\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(1, 4, True, True, True)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('parity max odd 5')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 17, "id": "structured-palace", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0, f)\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{}\n", "<0>\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(1, 0, True, True, True)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('f')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": 18, "id": "plain-modern", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0, t)\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "zielonka_tree\n", "\n", "\n", "\n", "0\n", "\n", "{}\n", "<0>\n", "\n", "\n", "\n" ], "text/plain": [ " >" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(1, 0, True, True, True)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = spot.acc_cond('t')\n", "print(c)\n", "t = spot.zielonka_tree(c)\n", "display(t)\n", "t.num_branches(), t.first_branch(), t.has_rabin_shape(), t.has_streett_shape(), t.has_parity_shape()" ] }, { "cell_type": "code", "execution_count": null, "id": "interesting-seller", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }