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A8

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Isaac Shoebottom 2024-04-11 23:20:56 -03:00
parent a8c763010a
commit 7c80576cc4
3 changed files with 95 additions and 0 deletions
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17
.idea/runConfigurations/Export_A7_No_Code.xml Normal file
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<component name="ProjectRunConfigurationManager">
<configuration default="false" name="Export A7 No Code" type="ShConfigurationType">
<option name="SCRIPT_TEXT" value="jupyter-nbconvert.exe &quot;Assignment 7.ipynb&quot; --to pdf --no-input" />
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<option name="SCRIPT_WORKING_DIRECTORY" value="$PROJECT_DIR$" />
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<option name="INTERPRETER_PATH" value="powershell.exe" />
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17
.idea/runConfigurations/Export_A8_No_Code.xml Normal file
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<component name="ProjectRunConfigurationManager">
<configuration default="false" name="Export A8 No Code" type="ShConfigurationType">
<option name="SCRIPT_TEXT" value="jupyter-nbconvert.exe &quot;Assignment 8.ipynb&quot; --to pdf --no-input" />
<option name="INDEPENDENT_SCRIPT_PATH" value="true" />
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61
Assignment 8.ipynb Normal file
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{
"cells": [
{
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"source": [
"# Question 48\n",
"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",
"\n",
"1. Start in M's start state\n",
"2. Go through the symbols of w one at a time\n",
"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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"id": "2d1690ef",
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"source": [
"$\\pagebreak$"
]
},
{
"cell_type": "markdown",
"id": "9a7c595f",
"metadata": {},
"source": [
"# Question 49\n",
"Let us assume that $EQ_{TM}$ is decidable, then we can:\n",
"\n",
"1. Pass two copies of $ALL_{TM}$ into $EQ_{TM}$\n",
"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",
"3. Therefor it is impossible for $EQ_{TM}$ to be decidable given that $ALL_{TM}$ is undecidable"
]
}
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