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hmk6 - are 2 occurences of ab and 2 occurences of ba 3 Let...

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COT 3100 Homework # 6 Fall 2000 Assigned: 11/21/00 Due: 11/30/00 1) Give regular expressions for each of the following languages: (Note: each language is over the alphabet L = {a,b} a) The language of all strings containing the substring ab. b) The language of all strings of length 3. c) The language of all strings with exactly 3 b’s. d) The set of all strings where every a is followed by 3 or more b’s. 2) Create a DFA to recognize the following languages over the alphabet L = {a,b}. a) The language of all strings of odd length. b) The language of all strings that contain exactly 2n a’s where n is an integer. c) The language of all strings that have the same number of substrings ab as substring ba. (So, for example, abaaabbba would be in this language since there
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Unformatted text preview: are 2 occurences of ab and 2 occurences of ba.) 3) Let T, W, and X be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if (T ∪ W)* = (T ∪ X)* then W = X. 4) Let T and W be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if T ⊆ W, then (TW)* ⊂ W*. Is it necessarily true that W* ⊂ (TW)*? Prove your answer. 5) Let T, W, and X be sets of strings over the alphabet L = {1,b}. Prove the following statement: ((TW)* ∪ (TX)*) ⊂ (T(W ∪ X))*. Is (T(W ∪ X))* ⊂ ((TW)* ∪ (TX)*)? Why or why not?...
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