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# hw04 - CS 154 Intro to Automata and Complexity Theory...

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CS 154 Intro. to Automata and Complexity Theory Handout 14 Autumn 2006 David Dill October 24, 2006 Problem Set 4 Due: October 31, 2006 Homework: (Total 100 points) Do the following exercises. Problem 1. [20 points] Consider the DFA given by the following transition table. 0 1 A B J B H C * C D G D E C * E F G F C E * G J C H B G I H E J H A Give the minimum equivalent DFA. For each state of the minimized DFA, specify the set of equiv- alent states of the original DFA. Problem 2. [15 points] Consider the (deterministic) Turing machine M given by M = ( { q 0 , q 1 , q 2 } , { a, b } , { a, b, B } , δ, q 0 , B, { q 2 } ) which has exactly four transitions defined in it, as described below. 1. δ ( q 0 , a ) = ( q 0 , B, R ) 2. δ ( q 0 , b ) = ( q 1 , B, R ) 3. δ ( q 1 , b ) = ( q 1 , B, R ) 4. δ ( q 1 , B ) = ( q 2 , B, R ) (a). [5 points] Specify the execution trace of M on the input string abb . (b). [5 points] Provide a regular expression for the language of this Turing machine. (c). [5 points] Suppose that we add the following transition to the above machine.

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hw04 - CS 154 Intro to Automata and Complexity Theory...

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