62 lines
1.6 KiB
Plaintext
62 lines
1.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "a90ef9f8022df10e",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"# Question 48\n",
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"Given that $A_{DFA}$ is decidable, and it will finish in a finite number of steps, we know that any DFA that accepts at least one string of finite length 3, we know that it is decidable. The algorithm is as follows:\n",
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"\n",
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"1. Start in M's start state\n",
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"2. Go through the symbols of w one at a time\n",
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"3. For all symbols of length 3, and the DFA is an accept state, we accept M DFA, otherwise reject M"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2d1690ef",
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"metadata": {},
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"source": [
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"$\\pagebreak$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9a7c595f",
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"metadata": {},
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"source": [
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"# Question 49\n",
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"Let us assume that $EQ_{TM}$ is decidable, then we can:\n",
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"\n",
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"1. Pass two copies of $ALL_{TM}$ into $EQ_{TM}$\n",
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"2. If $EQ_{TM}$ accepts the two copies of $ALL_{TM}$, this means that $ALL_{TM}$ is decidable, as $EQ_{TM}$ must decide on $ALL_{TM}$\n",
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"3. Therefor it is impossible for $EQ_{TM}$ to be decidable given that $ALL_{TM}$ is undecidable"
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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",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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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": "ipython2",
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"version": "2.7.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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