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Additional 9-14 Prove that the language {a"b" n, k ε N and n S k} is...
Additional 9-13 Prove that the language {w#w|w is a string over the alphabet {a,b,c}} is not...
Additional 9-13 Prove that the language {w#w|w is a string over the alphabet {a,b,c}} is not regular Tip: here are some strings in that language: abbc#abbc a#a aaa#aaa aaab#aaab cab#cab
Exercise 4.1.1: Prove that the following are not regular languages a) (0"1n|n 2 1). This language,...
Exercise 4.1.1: Prove that the following are not regular languages a) (0"1n|n 2 1). This language, consisting of a string of 0's followed by an cqual-length string of 1's, is the language Loi we considered informally at the beginning of the scction. Here, you should apply the pumping lemma in the proof. b) The set of strings of balanced parentheses. These are the strings of char- acters "(" and " that can appear in a well-formed arithmetic expression *c) O"IO"...
Let L be the language over {a, b, c} accepting all strings so that:
1. Let L be the language over {a, b, c} accepting all strings so that: 1. No b's occur before the first c. 2. No a's occur after the first c. 3. The last symbol of the string is b. 4. Each b that is not the last symbol is immediately followed by at least two d's. Choose any constructive method you wish, and demonstrate that L is regular. You do not need an inductive proof, but you should explain how your construction accounts for...
Prove that the following are not regular languages. Just B and F please Prove that the...
Prove that the following are not regular languages. Just B and F
please
Prove that the following are not regular languages. {0^n1^n | n Greaterthanorequalto 1}. This language, consisting of a string of 0's followed by an equal-length string of l's, is the language L_01 we considered informally at the beginning of the section. Here, you should apply the pumping lemma in the proof. The set of strings of balanced parentheses. These are the strings of characters "(" and ")"...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is not regular. (Note: na(w) and nu(w) are the number of a's and 's in tw, respectively.) To show this language is not regular, suppose you are given p. You now have complete choice of w. So choose wa+1, Of course you see how this satisfies the requirements of words in the language. Now, answer the following: (a) What is the largest value of lryl?...
1. (15) Let L be the language over {a,b,c} accepting all strings so that: 1. No...
1. (15) Let L be the language over {a,b,c} accepting all strings so that: 1. No b's occur before the first c. 2. No a's occur after the first c. 3. The last symbol of the string is b. 4. Each b that is not the last symbol is immediately followed by at least two c's. Choose any constructive method you wish, and demonstrate that is regular. You do not need an inductive proof, but you should explain how your...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b)...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
9. Mark the best description (smallest language class) for each of the following lang • R...
9. Mark the best description (smallest language class) for each of the following lang • R if it is regular • C if it is context free, but not regular . N if it is "bigger than" context free You do not have to prove your answer. L = {www: we {a,b}"} L2 = {a" : n > 2, m < 5} L3 = {a"m : n + m is even } LA = {w:na(w) + no(w) = n(w)} Ls...
E={a,b,c,d}, L = {anbmchdm : n, m 2 0}. For example, s = aabccd e L...
E={a,b,c,d}, L = {anbmchdm : n, m 2 0}. For example, s = aabccd e L because the symbols are in Unicode order, and #a(s) = #c(s), #(s) #c(s), #b(s) = #a(s); ac e L for the same reason; s = abcdd & L because #b(s) #a(s); and acbd & L beause the symbols are not in Unicode order. Prove that L & CFLs using the CF pumping theorem, starting by defining w such we Land |w| 2 k. Remember...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular real number multiplication), prove that On is a binary operation on Zn. That is, (Hint your proof will be very similar to the proof for homework 4 problem 7ab) (b) Let n E Z. Is the binary algebraic structure 〈L,On) always a group? Explain. (c) Prove There exists be Zn such that a n I if and only if (a, n)1. (d) It is...
Exercise 4.1.1: Prove that the following are not regular languages a) (0"1n|n 2 1). This language, consisting of a string of 0's followed by an cqual-length string of 1's, is the language Loi we considered informally at the beginning of the scction. Here, you should apply the pumping lemma in the proof. b) The set of strings of balanced parentheses. These are the strings of char- acters "(" and " that can appear in a well-formed arithmetic expression *c) O"IO"...
1. Let L be the language over {a, b, c} accepting all strings so that: 1. No b's occur before the first c. 2. No a's occur after the first c. 3. The last symbol of the string is b. 4. Each b that is not the last symbol is immediately followed by at least two d's. Choose any constructive method you wish, and demonstrate that L is regular. You do not need an inductive proof, but you should explain how your construction accounts for...
Prove that the following are not regular languages. Just B and F
please
Prove that the following are not regular languages. {0^n1^n | n Greaterthanorequalto 1}. This language, consisting of a string of 0's followed by an equal-length string of l's, is the language L_01 we considered informally at the beginning of the section. Here, you should apply the pumping lemma in the proof. The set of strings of balanced parentheses. These are the strings of characters "(" and ")"...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is not regular. (Note: na(w) and nu(w) are the number of a's and 's in tw, respectively.) To show this language is not regular, suppose you are given p. You now have complete choice of w. So choose wa+1, Of course you see how this satisfies the requirements of words in the language. Now, answer the following: (a) What is the largest value of lryl?...
1. (15) Let L be the language over {a,b,c} accepting all strings so that: 1. No b's occur before the first c. 2. No a's occur after the first c. 3. The last symbol of the string is b. 4. Each b that is not the last symbol is immediately followed by at least two c's. Choose any constructive method you wish, and demonstrate that is regular. You do not need an inductive proof, but you should explain how your...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
9. Mark the best description (smallest language class) for each of the following lang • R if it is regular • C if it is context free, but not regular . N if it is "bigger than" context free You do not have to prove your answer. L = {www: we {a,b}"} L2 = {a" : n > 2, m < 5} L3 = {a"m : n + m is even } LA = {w:na(w) + no(w) = n(w)} Ls...
E={a,b,c,d}, L = {anbmchdm : n, m 2 0}. For example, s = aabccd e L because the symbols are in Unicode order, and #a(s) = #c(s), #(s) #c(s), #b(s) = #a(s); ac e L for the same reason; s = abcdd & L because #b(s) #a(s); and acbd & L beause the symbols are not in Unicode order. Prove that L & CFLs using the CF pumping theorem, starting by defining w such we Land |w| 2 k. Remember...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular real number multiplication), prove that On is a binary operation on Zn. That is, (Hint your proof will be very similar to the proof for homework 4 problem 7ab) (b) Let n E Z. Is the binary algebraic structure 〈L,On) always a group? Explain. (c) Prove There exists be Zn such that a n I if and only if (a, n)1. (d) It is...
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