From 54c399dcb3ae8580005f1b806dcd4c837f540e8b Mon Sep 17 00:00:00 2001 From: Isaac Shoebottom Date: Fri, 16 Feb 2024 20:52:28 -0400 Subject: [PATCH] Add assignment 4 --- .idea/runConfigurations/Export_A4_No_Code.xml | 17 + Assignment 4.ipynb | 495 ++++++++++++++++++ Drawing/A4.xcf | Bin 0 -> 687747 bytes 3 files changed, 512 insertions(+) create mode 100644 .idea/runConfigurations/Export_A4_No_Code.xml create mode 100644 Assignment 4.ipynb create mode 100644 Drawing/A4.xcf diff --git a/.idea/runConfigurations/Export_A4_No_Code.xml b/.idea/runConfigurations/Export_A4_No_Code.xml new file mode 100644 index 0000000..4fd10f6 --- /dev/null +++ b/.idea/runConfigurations/Export_A4_No_Code.xml @@ -0,0 +1,17 @@ + + + + \ No newline at end of file diff --git a/Assignment 4.ipynb b/Assignment 4.ipynb new file mode 100644 index 0000000..e8479f7 --- /dev/null +++ b/Assignment 4.ipynb @@ -0,0 +1,495 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "initial_id", + "metadata": { + "collapsed": true, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.367829600Z", + "start_time": "2024-02-17T00:51:01.209832800Z" + } + }, + "outputs": [], + "source": [ + "# Helpers and imports\n", + "from automata.fa.nfa import NFA\n", + "\n", + "debug = False\n", + "\n", + "def nfa_test(nfa: NFA, str_arr: list[str]):\n", + " for s in str_arr:\n", + " if s == \"\":\n", + " print(f'ε is accepted: {nfa.accepts_input(s)}')\n", + " else:\n", + " print(f'{s} is accepted: {nfa.accepts_input(s)}')" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Q22\n", + "## (a)" + ], + "metadata": { + "collapsed": false + }, + "id": "2a3d28941b3eac7d" + }, + { + "cell_type": "code", + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n\n\n\n\n\n\nef361926-1987-4988-9833-4dc84f84fd2e\n\n\n\n\n\n\n\nq0\n\nq0\n\n\n\nef361926-1987-4988-9833-4dc84f84fd2e->q0\n\n\n\n\n\n\n\n\nq1\n\nq1\n\n\n\nq0->q1\n\n\n0\n\n\n\nq2\n\nq2\n\n\n\nq1->q2\n\n\n1\n\n\n\nq3\n\nq3\n\n\n\nq2->q3\n\n\n1\n\n\n\nq3->q3\n\n\n0,1\n\n\n\nq4\n\nq4\n\n\n\nq3->q4\n\n\n0\n\n\n\nq5\n\nq5\n\n\n\nq4->q5\n\n\n0\n\n\n\nq6\n\n\nq6\n\n\n\nq5->q6\n\n\n0\n\n\n\n", + "text/plain": ">" + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q22a = NFA(\n", + " states={'q0', 'q1', 'q2', 'q3', 'q4', 'q5', 'q6'},\n", + " input_symbols={'0', '1'},\n", + " transitions={\n", + " 'q0': {'0': {'q1'}},\n", + " 'q1': {'1': {'q2'}},\n", + " 'q2': {'1': {'q3'}},\n", + " 'q3': {'0': {'q3', 'q4'}, '1': {'q3'}},\n", + " 'q4': {'0': {'q5'}},\n", + " 'q5': {'0': {'q6'}}\n", + " },\n", + " initial_state='q0',\n", + " final_states={'q6'}\n", + ")\n", + "# Should be true\n", + "t = [\n", + " \"011000\",\n", + " \"0110000\",\n", + " \"011010000\",\n", + " \"011011010000\"\n", + "]\n", + "# Should be false\n", + "f = [\n", + " \"\",\n", + " \"0\",\n", + " \"1\",\n", + " \"0110\",\n", + " \"0110001\",\n", + " \"011010001\",\n", + " \"011011010001\"\n", + "]\n", + "if debug:\n", + " nfa_test(q22a, t)\n", + " print('-'*20)\n", + " nfa_test(q22a, f)\n", + "q22a.show_diagram()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.419829300Z", + "start_time": "2024-02-17T00:51:01.419829300Z" + } + }, + "id": "8ec96b76671bd51f", + "execution_count": 2 + }, + { + "cell_type": "markdown", + "source": [ + "## (b)" + ], + "metadata": { + "collapsed": false + }, + "id": "4c318b8332558fe6" + }, + { + "cell_type": "code", + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n\n\n\n\n\n\nb36964c3-7cac-44c2-80ec-5a57927f24cb\n\n\n\n\n\n\n\nq0\n\nq0\n\n\n\nb36964c3-7cac-44c2-80ec-5a57927f24cb->q0\n\n\n\n\n\n\n\n\nq3\n\nq3\n\n\n\nq0->q3\n\n\nc\n\n\n\nq1\n\nq1\n\n\n\nq0->q1\n\n\na\n\n\n\nq2\n\nq2\n\n\n\nq0->q2\n\n\nb\n\n\n\nq3->q3\n\n\na,b,c\n\n\n\nq4\n\n\nq4\n\n\n\nq3->q4\n\n\nc\n\n\n\nq1->q1\n\n\na,b,c\n\n\n\nq1->q4\n\n\na\n\n\n\nq2->q2\n\n\na,b,c\n\n\n\nq2->q4\n\n\nb\n\n\n\n", + "text/plain": ">" + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q22b = NFA(\n", + " states={'q0', 'q1', 'q2', 'q3', 'q4'},\n", + " input_symbols={'a', 'b', 'c'},\n", + " transitions={\n", + " 'q0': {'a': {'q1'}, 'b': {'q2'}, 'c': {'q3'}},\n", + " 'q1': {'a': {'q1', 'q4'}, 'b': {'q1'}, 'c': {'q1'}},\n", + " 'q2': {'a': {'q2'}, 'b': {'q2', 'q4'}, 'c': {'q2'}},\n", + " 'q3': {'a': {'q3'}, 'b': {'q3'}, 'c': {'q3', 'q4'}},\n", + " 'q4': {}\n", + " },\n", + " initial_state='q0',\n", + " final_states={'q4'}\n", + ")\n", + "\n", + "# Should be true\n", + "t = [\n", + " \"aa\",\n", + " \"bb\",\n", + " \"cc\",\n", + " \"aba\",\n", + " \"bab\",\n", + " \"cac\",\n", + " \"aabca\",\n", + " \"bcbab\",\n", + " \"ccccc\",\n", + "]\n", + "f = [\n", + " \"\",\n", + " \"a\",\n", + " \"b\",\n", + " \"c\",\n", + " \"abc\",\n", + " \"ab\",\n", + " \"bc\",\n", + " \"ca\",\n", + " \"ac\",\n", + " \"ba\",\n", + " \"abbbbbc\",\n", + " \"aaaaaaaaaaaabbbbbbbbbbbbcccccccccccccccc\",\n", + " \"abcabac\",\n", + " \"bbbbbbbbbbba\",\n", + "]\n", + "if debug:\n", + " nfa_test(q22b, t)\n", + " print('-'*20)\n", + " nfa_test(q22b, f)\n", + "q22b.show_diagram()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.425828900Z", + "start_time": "2024-02-17T00:51:01.419829300Z" + } + }, + "id": "b36d3c2c58fe93b7", + "execution_count": 3 + }, + { + "cell_type": "markdown", + "source": [ + "$\\pagebreak$" + ], + "metadata": { + "collapsed": false + }, + "id": "5a3996c26ce8cfbc" + }, + { + "cell_type": "markdown", + "source": [ + "# Q23" + ], + "metadata": { + "collapsed": false + }, + "id": "9551c6ce7a0990" + }, + { + "cell_type": "code", + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n\n\n\n\n\n\nc6536698-09e6-4b0c-b9c0-932845697f5e\n\n\n\n\n\n\n\nq0\n\nq0\n\n\n\nc6536698-09e6-4b0c-b9c0-932845697f5e->q0\n\n\n\n\n\n\n\n\nq1\n\nq1\n\n\n\nq0->q1\n\n\nε\n\n\n\nq5\n\nq5\n\n\n\nq0->q5\n\n\nε\n\n\n\nq1->q1\n\n\n0,1\n\n\n\nq2\n\nq2\n\n\n\nq1->q2\n\n\n0\n\n\n\nq3\n\nq3\n\n\n\nq1->q3\n\n\n1\n\n\n\nq6\n\nq6\n\n\n\nq5->q6\n\n\n0,1\n\n\n\nq4\n\n\nq4\n\n\n\nq2->q4\n\n\n0\n\n\n\nq3->q4\n\n\n1\n\n\n\nq7\n\n\nq7\n\n\n\nq6->q7\n\n\n0,1\n\n\n\nq7->q5\n\n\n0,1\n\n\n\n", + "text/plain": ">" + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q23 = NFA(\n", + " states={'q0', 'q1', 'q2', 'q3', 'q4', 'q5', 'q6', 'q7'},\n", + " input_symbols={'0', '1'},\n", + " transitions={\n", + " 'q0': {'': {'q1', 'q5'}},\n", + " 'q1': {'0': {'q1', 'q2'}, '1': {'q1', 'q3'}},\n", + " 'q2': {'0': {'q4'}},\n", + " 'q3': {'1': {'q4'}},\n", + " 'q5': {'0': {'q6'}, '1': {'q6'}},\n", + " 'q6': {'0': {'q7'}, '1': {'q7'}},\n", + " 'q7': {'0': {'q5'}, '1': {'q5'}}\n", + " },\n", + " initial_state='q0',\n", + " final_states={'q4', 'q7'}\n", + ")\n", + "t = [\n", + " '00',\n", + " '11',\n", + " '01',\n", + " '00000',\n", + " '11111',\n", + " '01010',\n", + " '01111100',\n", + " '10010111',\n", + " '011100',\n", + " '10010',\n", + " '10001011',\n", + "]\n", + "f = [\n", + " '',\n", + " '0',\n", + " '1',\n", + " '101',\n", + " '010',\n", + " '0001',\n", + " '1110',\n", + " '0101',\n", + " '0111110',\n", + "]\n", + "if debug:\n", + " nfa_test(q23, t)\n", + " print('-'*20)\n", + " nfa_test(q23, f)\n", + "q23.show_diagram()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.456829Z", + "start_time": "2024-02-17T00:51:01.428830800Z" + } + }, + "id": "7055f3d7e013c8bf", + "execution_count": 4 + }, + { + "cell_type": "markdown", + "source": [ + "$\\pagebreak$" + ], + "metadata": { + "collapsed": false + }, + "id": "35ed9908c8809b00" + }, + { + "cell_type": "markdown", + "source": [ + "# Q24\n", + "## (a) \n", + "The language for this graph is:\n", + "$$L = \\{ w \\in \\{ 0, 1, 2 \\}^* \\ | \\text{ The fourth last symbol in } w \\text{ is } 0 \\text { and the second last symbol in } w \\text{ is } 2 \\}$$\n", + "\n", + "## (b)\n", + "The language for this graph is:\n", + "$$L = \\{ w \\in \\{ a, b, c \\}^* \\ | \\ w \\text{ contains the substring } ab \\text { or } w \\text{ contains the substring } ac \\}$$" + ], + "metadata": { + "collapsed": false + }, + "id": "d359a31d044ce735" + }, + { + "cell_type": "markdown", + "source": [ + "$\\pagebreak$" + ], + "metadata": { + "collapsed": false + }, + "id": "144bcb36426add4a" + }, + { + "cell_type": "markdown", + "source": [ + "# Q26\n", + "## (a)" + ], + "metadata": { + "collapsed": false + }, + "id": "233aa8019cdbe103" + }, + { + "cell_type": "code", + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n\n\n\n\n\n\n395dc4d0-bf07-4c32-b931-cf10ac1006e5\n\n\n\n\n\n\n\nq00\n\nq00\n\n\n\n395dc4d0-bf07-4c32-b931-cf10ac1006e5->q00\n\n\n\n\n\n\n\n\nq00->q00\n\n\na,b,c,d\n\n\n\nq01\n\nq01\n\n\n\nq00->q01\n\n\na\n\n\n\nq02\n\nq02\n\n\n\nq00->q02\n\n\nb\n\n\n\nq03\n\nq03\n\n\n\nq00->q03\n\n\nc\n\n\n\nq04\n\nq04\n\n\n\nq00->q04\n\n\nd\n\n\n\nq05\n\nq05\n\n\n\nq01->q05\n\n\na\n\n\n\nq06\n\nq06\n\n\n\nq02->q06\n\n\nb\n\n\n\nq07\n\nq07\n\n\n\nq03->q07\n\n\nc\n\n\n\nq08\n\nq08\n\n\n\nq04->q08\n\n\nd\n\n\n\nq09\n\nq09\n\n\n\nq05->q09\n\n\na\n\n\n\nq10\n\nq10\n\n\n\nq06->q10\n\n\nb\n\n\n\nq11\n\nq11\n\n\n\nq07->q11\n\n\nc\n\n\n\nq12\n\nq12\n\n\n\nq08->q12\n\n\nd\n\n\n\nq13\n\n\nq13\n\n\n\nq09->q13\n\n\na\n\n\n\nq10->q13\n\n\nb\n\n\n\nq11->q13\n\n\nc\n\n\n\nq12->q13\n\n\nd\n\n\n\nq13->q13\n\n\na,b,c,d\n\n\n\n", + "text/plain": ">" + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q26a = NFA(\n", + "\tstates={'q00', 'q01', 'q02', 'q03', 'q04', 'q05', 'q06', 'q07', 'q08', 'q09', 'q10', 'q11', 'q12', 'q13'},\n", + " input_symbols={'a', 'b', 'c', 'd'},\n", + " transitions={\n", + " 'q00': {'a': {'q00', 'q01'}, 'b': {'q00', 'q02'}, 'c': {'q00', 'q03'}, 'd': {'q00', 'q04'}},\n", + " 'q01': {'a': {'q05'}},\n", + " 'q02': {'b': {'q06'}},\n", + " 'q03': {'c': {'q07'}},\n", + " 'q04': {'d': {'q08'}},\n", + "\t 'q05': {'a': {'q09'}},\n", + " 'q06': {'b': {'q10'}},\n", + " 'q07': {'c': {'q11'}},\n", + " 'q08': {'d': {'q12'}},\n", + " 'q09': {'a': {'q13'}},\n", + " 'q10': {'b': {'q13'}},\n", + " 'q11': {'c': {'q13'}},\n", + " 'q12': {'d': {'q13'}},\n", + " 'q13': {'a': {'q13'}, 'b': {'q13'}, 'c': {'q13'}, 'd': {'q13'}},\n", + " },\n", + " initial_state='q00',\n", + " final_states={'q13'},\n", + ")\n", + "t = [\n", + " 'aaaa',\n", + " 'bbbb',\n", + " 'cccc',\n", + " 'dddd',\n", + " 'abbbba',\n", + " 'acccca',\n", + " 'adddda',\n", + " 'abbbbabbbba',\n", + " 'accccacccca',\n", + " 'addddadddda',\n", + " 'aaabbbcccdddd',\n", + "]\n", + "f = [\n", + " 'abcd',\n", + " 'abdc',\n", + " 'acbd',\n", + " 'acdb',\n", + " 'aaabb',\n", + " 'abbbc',\n", + " 'abbbd',\n", + "]\n", + "if debug:\n", + " nfa_test(q26a, t)\n", + " print('-'*20)\n", + " nfa_test(q26a, f)\n", + "q26a.show_diagram()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.510831200Z", + "start_time": "2024-02-17T00:51:01.457831400Z" + } + }, + "id": "ba55249fa215010e", + "execution_count": 5 + }, + { + "cell_type": "markdown", + "source": [ + "## (b)" + ], + "metadata": { + "collapsed": false + }, + "id": "c55b1fd818f8da4e" + }, + { + "cell_type": "code", + "outputs": [ + { + "data": { + "image/svg+xml": "\n\n\n\n\n\n\n\n\n9a93236f-ac2b-4384-8c2a-d9686587f8ad\n\n\n\n\n\n\n\nq0\n\n\nq0\n\n\n\n9a93236f-ac2b-4384-8c2a-d9686587f8ad->q0\n\n\n\n\n\n\n\n\nq1\n\nq1\n\n\n\nq0->q1\n\n\na\n\n\n\nq5\n\n\nq5\n\n\n\nq0->q5\n\n\nb\n\n\n\nq2\n\nq2\n\n\n\nq1->q2\n\n\na\n\n\n\nq3\n\n\nq3\n\n\n\nq1->q3\n\n\nb\n\n\n\nq5->q5\n\n\nb\n\n\n\nq6\n\nq6\n\n\n\nq5->q6\n\n\nc\n\n\n\nq2->q1\n\n\na\n\n\n\nq4\n\nq4\n\n\n\nq3->q4\n\n\nb\n\n\n\nq7\n\nq7\n\n\n\nq6->q7\n\n\nc\n\n\n\nq4->q3\n\n\nb\n\n\n\nq8\n\n\nq8\n\n\n\nq7->q8\n\n\nc\n\n\n\nq8->q6\n\n\nc\n\n\n\n", + "text/plain": ">" + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q26b = NFA(\n", + "\tstates={'q0', 'q1', 'q2', 'q3', 'q4', 'q5', 'q6', 'q7', 'q8'},\n", + "\tinput_symbols={'a', 'b', 'c'},\n", + "\ttransitions={\n", + "\t\t'q0': {'a': {'q1'}, 'b': {'q5'}},\n", + "\t\t'q1': {'a': {'q2'}, 'b': {'q3'}},\n", + "\t\t'q2': {'a': {'q1'}},\n", + "\t\t'q3': {'b': {'q4'}},\n", + "\t\t'q4': {'b': {'q3'}},\n", + "\t\t'q5': {'b': {'q5'}, 'c': {'q6'}},\n", + "\t\t'q6': {'c': {'q7'}},\n", + "\t\t'q7': {'c': {'q8'}},\n", + "\t\t'q8': {'c': {'q6'}},\n", + "\t},\n", + "\tinitial_state='q0',\n", + "\tfinal_states={'q0', 'q3', 'q5', 'q8'},\n", + ")\n", + "t = [\n", + " 'ab',\n", + " 'aaabbb',\n", + " 'aaaaabbbbb',\n", + " 'b',\n", + " 'bb',\n", + " 'bbccc',\n", + " 'bbcccccc',\n", + "]\n", + "f = [\n", + " 'a',\n", + " 'aaa',\n", + " 'aaaa',\n", + " 'bba',\n", + " 'ca',\n", + " 'cb',\n", + " 'cc',\n", + " 'ccca',\n", + " 'bbba',\n", + " 'bbbbbc',\n", + "]\n", + "if debug:\n", + " nfa_test(q26b, t)\n", + " print('-'*20)\n", + " nfa_test(q26b, f)\n", + "\n", + "q26b.show_diagram()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-02-17T00:51:01.566831900Z", + "start_time": "2024-02-17T00:51:01.509831400Z" + } + }, + "id": "b44d21890b7c5fe6", + "execution_count": 6 + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": 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