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hw03 - CS 154 Intro to Automata and Complexity Theory...

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CS 154 Intro. to Automata and Complexity Theory Handout 10 Autumn 2009 David Dill October 13, 2009 Problem Set 3 Due: October 20, 2009 Homework: (Total 100 points) Do the following exercises. Problem 1. [30 points] Give an algorithm to solve the following decision problems. In each case you can assume that you are given a concrete rep- resentation of the language in the form of a DFA. You must justify the correctness of the algorithm to receive full credit. a). Suppose L is a regular language over the alphabet Σ = { 0 , 1 } . Give an algorithm to decide whether | L | ≥ 100. b). Suppose L is a regular language over the alphabet Σ = { 0 , 1 } . Give an algorithm to decide whether L contains any string w such that w has zero occurrences of the patterns 00 and 11. Problem 2. [10 points] Show how to modify the product construction for DFAs, discussed in class, such that the resulting DFA accepts the union, as opposed to the intersection, of the languages of the two given DFAs. Prove that your construction is correct. ( Hint : Refer to the discussion of the

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