key6sp00 - COT3100, Spring 2000 S. Lang Solution Key to...

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COT3100, Spring 2000 S. Lang Solution Key to Assignment #6 (Optional) 4/24/2000 1. Give a regular expression for each of the following languages (no proof or explanation is required): (a) The set of strings over { a , b } that do not contain the substring ba and do not contain the substring ab . a * + b *. (Intuitively, this answer is because the set contains strings λ , a , aa , aaa , …, b , bb , bbb , etc. That is, the set contains symbols a ’s by themselves, or symbol b ’s by themselves, but never a and b mixed together.) (b) The set of strings over { a , b } that have a length divisible by 3. (( a + b )( a + b )( a + b ))*, i.e., ( aaa + aab + aba + abb + baa + bab + bba + bbb )*. (c) The set of strings over { a , b , c } that have exactly two occurrences of symbol a (no restrictions on th occurrences of symbols b or c ). ( b + c )* a ( b + c )* a ( b + c )*. 2. Prove the following identities of regular expressions using appropriate rules and properties. Explain each step of your proof. (a)
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key6sp00 - COT3100, Spring 2000 S. Lang Solution Key to...

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