A7
This commit is contained in:
parent
fb72fe93c6
commit
a8c763010a
@ -8,7 +8,7 @@
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"from automata.fa.nfa import NFA\n",
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"from IPython.display import Math\n",
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"\n",
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"debug = False\n",
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"debug = True\n",
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"\n",
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"def regex_test(regex: str, inputs: list[str]):\n",
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" re.validate(regex)\n",
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@ -30,8 +30,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.229475Z",
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"start_time": "2024-03-02T00:28:44.047364Z"
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"end_time": "2024-03-22T22:22:26.498255Z",
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"start_time": "2024-03-22T22:22:26.217210Z"
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}
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},
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"id": "aa9fd8c82c66ac9a",
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@ -39,7 +39,17 @@
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},
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{
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"cell_type": "code",
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"{'aaaab', 'a', 'b', 'aaab', 'ab', 'aaaa', 'aab'}\n",
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"['baaaa', 'ba', 'baab', 'baaaaa', 'baa', 'baaab']\n",
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"['', 'b', 'bb', 'bbb', 'bba', 'ba', 'bab']\n"
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]
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}
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],
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"source": [
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"l1 = ['b', 'ba']\n",
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"l2 = ['a', 'aab', 'aaaa']\n",
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@ -79,8 +89,8 @@
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"metadata": {
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"collapsed": true,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.236163Z",
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"start_time": "2024-03-02T00:28:44.231091Z"
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"end_time": "2024-03-22T22:22:26.505139Z",
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"start_time": "2024-03-22T22:22:26.499628Z"
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}
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},
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"id": "initial_id",
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@ -131,6 +141,17 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"aabb: False\n",
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"aabbbb: False\n",
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"aabbbbb: True\n",
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"aaabbbbbb: False\n",
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"aaaabbbbbbbbb: True\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -158,8 +179,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.245325Z",
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"start_time": "2024-03-02T00:28:44.237457Z"
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"end_time": "2024-03-22T22:22:26.515494Z",
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"start_time": "2024-03-22T22:22:26.506412Z"
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}
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},
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"id": "c0d81b8fb61431de",
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@ -178,6 +199,22 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"ab: True\n",
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"bab: False\n",
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"bbab: True\n",
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"bbbabb: True\n",
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"bbbabbb: False\n",
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"abb: False\n",
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"abbb: True\n",
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"ba: True\n",
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"bba: False\n",
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"bbba: True\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -210,8 +247,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.251244Z",
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"start_time": "2024-03-02T00:28:44.246625Z"
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"end_time": "2024-03-22T22:22:26.522964Z",
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"start_time": "2024-03-22T22:22:26.517188Z"
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}
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},
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"id": "75f2af38daefc05b",
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@ -241,6 +278,36 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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": True\n",
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"0: True\n",
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"1: True\n",
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"00: True\n",
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"01: True\n",
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"10: True\n",
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"11: True\n",
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"000: True\n",
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"001: True\n",
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"010: True\n",
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"011: True\n",
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"100: True\n",
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"101: True\n",
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"0000: True\n",
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"0001: True\n",
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"0010: True\n",
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"0011: True\n",
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"0100: True\n",
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"0101: True\n",
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"0110: True\n",
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"0111: True\n",
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"1000: True\n",
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"00000: False\n",
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"11111: False\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -287,8 +354,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.258942Z",
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"start_time": "2024-03-02T00:28:44.253012Z"
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"end_time": "2024-03-22T22:22:26.531449Z",
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"start_time": "2024-03-22T22:22:26.524511Z"
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}
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},
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"id": "404b569fb1f1b3dd",
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@ -307,6 +374,17 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0100001: True\n",
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"0100000100001: True\n",
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"1000001: True\n",
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"00000010000100000: True\n",
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"1000100001: False\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -336,8 +414,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.265618Z",
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"start_time": "2024-03-02T00:28:44.260279Z"
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"end_time": "2024-03-22T22:22:26.538114Z",
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"start_time": "2024-03-22T22:22:26.532887Z"
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}
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},
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"id": "91ecde46ccfd6037",
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@ -366,6 +444,15 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"00100: True\n",
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"00100: True\n",
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"00100: False\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -380,6 +467,7 @@
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"# Let R1 be the regular expression 1* 0 1* 0 1* 0 1* 0 1*\n",
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"# Let R2 be the regular expression 0* (1 ∪ ε) 0* (1 ∪ ε) 0* (1 ∪ ε) 0* (1 ∪ ε) 0*\n",
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"# Let R3 be the regular expression (0 ∪ 1)* 00 (0 ∪ 1)\n",
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"# Was not supposed to be accepted by all, only bt 2 and 3\n",
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"r1 = '1*01*01*01*01*'\n",
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"r2 = '0*(1|())0*(1|())0*(1|())0*(1|())0*'\n",
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"r3 = '(0|1)*00(0|1)'\n",
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@ -393,8 +481,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.272009Z",
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"start_time": "2024-03-02T00:28:44.267238Z"
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"end_time": "2024-03-22T22:22:26.547221Z",
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"start_time": "2024-03-22T22:22:26.539392Z"
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}
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},
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"id": "e3c432e6556167c7",
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@ -423,6 +511,22 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"p: True\n",
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"cp: True\n",
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"pc: True\n",
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"cpc: True\n",
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"ccpcc: True\n",
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"ccpccpcc: True\n",
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"ccpccpccpcc: True\n",
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"ccpccpccpccpcc: True\n",
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"cpcpcpcpcpc: True\n",
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"pp: True\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -446,7 +550,7 @@
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" 'ccpccpccpcc',\n",
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" 'ccpccpccpccpcc',\n",
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" 'cpcpcpcpcpc',\n",
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" '',\n",
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" 'pp', # Not supposed to be here\n",
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"]\n",
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"if debug:\n",
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" regex_test(q33, inputs)\n",
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@ -455,8 +559,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.278114Z",
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"start_time": "2024-03-02T00:28:44.273285Z"
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"end_time": "2024-03-22T22:22:26.555155Z",
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"start_time": "2024-03-22T22:22:26.549229Z"
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}
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},
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"id": "5b8c9ad34523ea81",
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@ -485,6 +589,25 @@
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{
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"cell_type": "code",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0: True\n",
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"1: True\n",
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"00: True\n",
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"01: True\n",
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"10: True\n",
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"11: True\n",
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"000: False\n",
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"001: False\n",
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"010: False\n",
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"0000: True\n",
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"00001: True\n",
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"001100: False\n",
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"011001110: False\n"
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]
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},
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{
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"data": {
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"text/plain": "<IPython.core.display.Math object>",
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@ -520,8 +643,8 @@
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-03-02T00:28:44.284200Z",
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"start_time": "2024-03-02T00:28:44.279548Z"
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"end_time": "2024-03-22T22:22:26.563180Z",
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"start_time": "2024-03-22T22:22:26.556508Z"
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}
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},
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"id": "6aa37e012a2b072d",
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135
Assignment 7.ipynb
Normal file
135
Assignment 7.ipynb
Normal file
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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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