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# key6fa00 - COT3100.01 Fall 2000 S Lang Solution Key to...

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COT3100.01, Fall 2000 S. Lang Solution Key to Assignment #6 (40 pts.) 11/30/2000 Let a , b , c denote distinct symbols for the following questions: 1. Give a regular expression for each of the following languages (no proof is required but brief explanations are encouraged): (a) The set of strings over { a , b } that contain exactly two occurrences of symbol a and at least one occurrence of symbol b . bb * ab * ab * + b * abb * ab * + b * ab * abb *. Explanation (FYI): The first term bb * ab * ab * represents those strings that contain two a ’s with at least one b before the first a ; similarly, the second term b * abb * ab * represents those strings that contain two a ’s with at least one b between the two a ’s; and the third term b * ab * abb * represents those strings that contain two a ’s with at least one b after the second a . (b) The set of strings over { a , b } that contain the substring aa but do not contain the substring bb . ( a *( baa *)* + a *( baa *)* b ) aa ( a *( baa *)* + a *( baa *)* b ). Explanation (FYI): The expression ( baa *)* is used to ensure each b (if any) is followed by at least one a before the next b ; therefore guaranteeing no occurrences of two consecutive b ’s. Thus, the term a *( baa *)* represents strings with possible leading a ’s but no occurrences of substring bb ; the other term a *( baa *)* b covers those strings with an ending single b .

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key6fa00 - COT3100.01 Fall 2000 S Lang Solution Key to...

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