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Unformatted text preview: Solutions for Problem Set 5 CS 373: Theory of Computation Assigned: October 5, 2010 Due on: October 12, 2010 at 10am Homework Problems Problem 1 . [Category: Comprehension+Design] Consider the following DFA M . Let L = L ( M ). q q 1 q 2 q 3 q 4 q 5 1 1 1 1 , 1 1 Figure 1: DFA M for Problem 1 1. What are the following sets: suffix( L, ), suffix( L, 0), suffix( L, 00), and suffix( L, 01)? [2 points] 2. What are the following sets: suffix( M,q ), suffix( M,q 2 ), suffix( M,q 3 ), and suffix( M,q 4 )? [2 points] 3. Construct the minimum DFA that is equivalent to M , showing the steps of the construction clearly. [3 points] 4. For every pair of states in the minimal DFA constructed in the previous part, give a string that “distinguishes” the states. [3 points] Solution: 1. suffix( L, ) = L 1 = L (1 * 0(00 ∪ 01 ∪ 1)(0 ∪ 1) * ), suffix( L, 0) = L 2 = L ((00 ∪ 01 ∪ 1)(0 ∪ 1) * ), suffix( L, 00) = L 3 = L ((0 ∪ 1)(0 ∪ 1) * ), suffix( L, 01) = L 4 = (0 ∪ ) * 2. suffix( M,q ) = L 1 , suffix( M,q 2 ) = L 2 , suffix( M,q 3 ) = L 3 , and suffix( M,q 4 ) = L 4 , where L 1 ,L 2 ,L 3 , and L 4 are the language defined in the previous part. 3. We will carry out the table filling algorithms outlined in class. In the tables below, if the entry corresponding to q i and q j is a , then it means that...
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 Fall '08
 Viswanathan,M
 Set Theory, Automata theory

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