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Rephrase q3

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Isaac Shoebottom 2024-01-19 14:00:50 -04:00
parent fd4359943e
commit cec9e9104f
1 changed files with 27 additions and 27 deletions
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Assignment 1.ipynb
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@ -19,8 +19,8 @@
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@ -398,9 +398,9 @@
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"source": [ "source": [
"First it could be helpful to find the set of all valid games to compare against. This is a little tricky as first you need to know the rules of the game and encode them correctly. The rules that I have discerned are as follows:\n", "First, it could be helpful to find the set of all valid games to compare against. This is a little tricky as first you need to know the rules of the game and encode them correctly as a language. The rules that I have discerned are as follows:\n",
"1. Each valid game has 3 a's or 3 b's, denoting a victory for one side\n", "1. Each valid game has 3 a's or 3 b's, denoting a victory for one side\n",
"2. Once it has either victories on either side, the game does not continue, and the string is complete\n", "2. Once either side has won, the game does not continue, and the string is complete\n",
"\n", "\n",
"$$L = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\text{ and } w \\text{ does not end with the opposite letter}\\}$$" "$$L = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\text{ and } w \\text{ does not end with the opposite letter}\\}$$"
] ]
@ -412,8 +412,8 @@
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@ -455,7 +455,7 @@
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"(a) $L_1 = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n", "(a) $L_1 = \\{w \\in \\{a,b\\}^* | n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n",
"\n", "\n",
"This one is not representable with code, as the set is produces is infinite. This language places no restrictions on the length of the string, so \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\" is a valid string in this language. So here is a few examples of valid strings in this language that are not valid in the original language L but are in this language:\n", "This language is not representable with code, as the set is produces is infinite. This language places no restrictions on the length of the string, so \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\" is a valid string in this language. So here is a few examples of valid strings in this language that are not valid in the original:\n",
"\n", "\n",
"1. \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\"\n", "1. \"aaabbbbbbbbbbbbbbbbbbbbbbbbbbb\"\n",
"2. \"bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaa\"\n", "2. \"bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaa\"\n",
@ -471,7 +471,7 @@
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"(b) $L_2 = \\{w \\in \\{a,b\\}^* | |w| \\leq 5, \\text{ and } n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n", "(b) $L_2 = \\{w \\in \\{a,b\\}^* | |w| \\leq 5, \\text{ and } n_a(w) = 3 \\text{ or } n_b(w) = 3 \\}$\n",
"\n", "\n",
"This language has the problem is not encoding the rule that the game stops once a player has 3 a's or 3 b's. This can be seen in these strings that are valid in this language but not in the original language L:" "This language differs as it is not encoding the rule that the game stops once a player has 3 a's or 3 b's. This can be seen in these strings that are valid in this language but not in the original language L:"
] ]
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@ -481,8 +481,8 @@
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@ -514,7 +514,7 @@
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"(c) $L_3 = \\{w \\in \\{a,b\\}^* | (n_a(w) = 3 \\text{ and } n_b(w) < 3) \\text{ or } (n_b(w) = 3 \\text{ and } n_a(w) < 3) \\}$\n", "(c) $L_3 = \\{w \\in \\{a,b\\}^* | (n_a(w) = 3 \\text{ and } n_b(w) < 3) \\text{ or } (n_b(w) = 3 \\text{ and } n_a(w) < 3) \\}$\n",
"\n", "\n",
"This language has a similar problem to the previous one, in that it does not encode the rule that the game stops once a player has 3 a's or 3 b's. The difference in this language is that the limit of string length 5 is not explicitly stated, however it is encoded to be that way by saying that if there are 3 a's then there must be less than 3 b's, and vice versa. This means that the effective maximum length of the string is 5, and thus the language is equivalent to the language from the previous question.\n", "This language is similar to the previous one, in that it does not encode the rule that the game stops once a player has 3 a's or 3 b's. The difference in this language is that the limit of string length 5 is not explicitly stated, however it is encoded to be that way by saying that if there are 3 a's then there must be less than 3 b's, and vice versa. This means that the effective maximum length of the string is 5, and thus the language is equivalent to the language from the previous question.\n",
"$$\n", "$$\n",
"x, y \\in \\mathbb{Z}^* \\\\\n", "x, y \\in \\mathbb{Z}^* \\\\\n",
"x = 3 \\\\\n", "x = 3 \\\\\n",
@ -531,8 +531,8 @@
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