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

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Unformatted text preview: 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. 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 , q 1 , q 2 } , { a, b } , { a, b, B } , , q , B, { q 2 } ) which has exactly four transitions defined in it, as described below. 1. ( q , a ) = ( q , B, R ) 2. ( q , b ) = ( q 1 , B, R ) 3. ( q 1 , b ) = ( q 1 , B, R ) 4. ( q 1 , B ) = ( q 2 , B, R ) (a). [5 points] Specify the execution trace of M on the input string abb ....
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hw04 - CS 154 Intro. to Automata and Complexity Theory...

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