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# hw_03_sol - Problem Set 3 Spring 10 Due Thursday Feb 18 in...

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Unformatted text preview: Problem Set 3 Spring 10 Due: Thursday Feb 18 in class before the lecture. Please follow the homework format guidelines posted on the class web page: http://www.cs.uiuc.edu/class/sp10/cs373/ 1. [ Category : Comprehension, Points : 20] Give a regular expression for the following languages: (a) Σ = { a,b } : The set of all strings where the second letter from the start and the end is an a . (b) Σ = { a,b } : The set of all strings that have both aa and bb as a substring. (c) Σ = { a,b,c } : The set of all strings, such that between any a and c there's at least one b . Describe the language of each of the following regular expressions in your own words. Please be speci c and try to minimize the amount of mathematical notation you use. (a) Σ = { a,b } . ( ab + ba ) * (b) Σ = { a,b } . (( a * ) b ( a * ) b ( a * )) * b (c) Σ = { a,b,c } . (( + a + aa + aaa )( b + c )) * ( + a + aa + aaa ) Solution: Give a regular expression for the following languages: (a) Σ = { a,b } : The set of all strings where the second letter from the start and the end is an a . Answer: ( a + b ) a ( a + b ) * a ( a + b ) (b) Σ = { a,b } : The set of all strings that have both aa and bb as a substring. Answer: (( a + b ) * aa ( a + b ) * bb ( a + b ) * ) + (( a + b ) * bb ( a + b ) * aa ( a + b ) * ) (c) Σ = { a,b,c } : The set of all strings, such that between any a and c there's at least one b . Answer: (( + aa * + cc * ) b ) * ( + aa * + cc * ) Describe the language of each of the following regular expressions in your own words. Please be speci c and try to minimize the amount of mathematical notation you use. (a) Σ = { a,b } . ( ab + ba ) * Answer: The set of all strings of a s and b s that have an equal amount of a s and b s....
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hw_03_sol - Problem Set 3 Spring 10 Due Thursday Feb 18 in...

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