136 lines
3.5 KiB
Plaintext
136 lines
3.5 KiB
Plaintext
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{
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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 42\n",
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"## c.\n",
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"$$S \\rightarrow 0S0 | 0S1 | 1S0 | 1S1 | 1$$\n",
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"\n",
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"## d.\n",
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"$$S \\rightarrow X | \\epsilon$$\n",
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"$$X \\rightarrow aXdd | Y$$\n",
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"$$Y \\rightarrow bYd | Z$$\n",
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"$$Z \\rightarrow cZ | \\epsilon$$\n",
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"\n",
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"## e.\n",
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"$$S \\rightarrow 0S | 1S | 00S | 01S | 10S | 11S | 000S | 001S | 010S | 011S| 100S | 101S | 111S | \\epsilon$$"
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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 43\n",
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"## a.\n",
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"$$B = \\{ w \\in \\{a, b, c\\}^* | |w| = 4n+1, n \\in \\mathbb{Z}^{\\text{nonneg}} \\}$$\n",
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"\n",
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"## b.\n",
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"$$B = \\{ 0^2x1^3y+2 | x, y \\in \\mathbb{Z}^{\\text{nonneg}} \\}$$\n",
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"\n",
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"## c.\n",
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"$$B = \\{ 0^x1^y | x \\neq y \\text{ and } x, y \\in \\mathbb{Z}^{\\text{nonneg}} \\}$$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c8d0ce5a",
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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": "8d439d76",
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"metadata": {},
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"source": [
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"# Question 44\n",
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"## a.\n",
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"$$B = \\{ 0^x1^y | y = x + 1 \\text{ and } x, y \\in \\mathbb{Z}^{\\text{nonneg}} \\}$$\n",
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"\n",
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"## c.\n",
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"$$B = \\{ 0^x1^y | y = 3x \\text{ and } x, y \\in \\mathbb{Z}^{\\text{nonneg}} \\}$$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "323bea35",
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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": "56466c7f",
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"metadata": {},
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"source": [
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"# Question 45\n",
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"1. First the machine should move left to right looking for a \"b\". If it does not find one it moves to the reject state and if it finds one it will:\n",
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" - Erase the \"b\"\n",
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" - Move back to the start\n",
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" - Look for an \"a\". If it finds one it will repeat step 1. If it does not find one, it will move to the accept state"
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]
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": "$\\pagebreak$",
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"id": "e9fba2ef63041f08"
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": [
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"# Question 47\n",
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"1. First the machine should check if the length of the string is at least 6 and if not, reject\n",
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"2. Copy 0 or more symbols to tape 2 from tape 1\n",
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"3. Erase all of tape 2\n",
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"4. Copy 3 symbols to tape 2 from tape 1\n",
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"5. Copy 0 or more symbols to tape 3 from tape 1\n",
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"6. Erase of all of tape 3\n",
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"7. Copy 3 symbols to tape 3 from tape 1\n",
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"8. Compare tapes 2 and 3 and if they match, accept, otherwise reject\n",
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"\n",
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"The nondeterminism of this machine is the copying 0 or more symbols, as this accounts for strings u and x, as they can be any length including 0, and the machine can make a choice of 0 or more."
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],
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"id": "7b6c771c1004546f"
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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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