compe330_hw2_sols

compe330_hw2_sols - COMP 330 Autumn 2006 Assignment 2...

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COMP 330 Autumn 2006 Assignment 2 Prakash Panangaden Solutions Question 1 [20 points] Give regular expressions for the following languages over { a, b } : 1. { w | w begins and ends with an a } . Solution: a + a ( a + b ) * a . 2. { w | every odd position is a b } . Solution: ( b ( a + b )) * b * . Note that “every odd position is a b does not imply that every even position is an a . 3. { w | w contains at least two a s and at most one b } . Solution: aaa * + aaa * b + aa * baa * + baaa * . 4. All strings except the empty string. Solution: a ( a + b ) * + b ( a + b ) * . Question 2 [20 points] Write Fnite automata that accept the following regular expressions: 1. ² + a ( a + b ) * + ( a + b ) * aa ( a + b ) * Solution a b a a,b b a b b a a,b 1
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2. [ ba + ( a + bb ) a * b ] * Solution b a b b a a Question 3 [20 points] Give a DFA that recognizes valid decimal numbers. These are numbers that have a decimal point and an optional positive or negative sign in front. There may be digits
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This note was uploaded on 12/01/2009 for the course COMP COMP 330 taught by Professor Panangaden during the Spring '04 term at McGill.

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compe330_hw2_sols - COMP 330 Autumn 2006 Assignment 2...

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