cs373 fa10 hw6sol - Solutions for Problem Set 6 CS 373:...

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Unformatted text preview: Solutions for Problem Set 6 CS 373: Theory of Computation Assigned: October 12, 2010 Due on: October 19, 2010 at 10am Homework Problems Problem 1 . [Category: Comprehension] Consider the following Turing Machine M with input alphabet = { a,b } . The reject state q rej is not shown, and if from a state there is no transition on some symbol then q q acc q 1 q 2 q 3 q 4 t t , R b X, R a X, R t t , R Y Y, R a X, R b X, R a a, R Y Y, R b Y, L b b, R Y Y, R a Y, L a a, L b b, L Y Y, L X X, R as per our convention, we assume it goes to the reject state. 1. Give the formal definition of M as a tuple. [3 points] 2. Describe each step of the computation of M on the input baabab as a sequence of instantaneous descriptions. [3 points] 3. Describe the language recognized by M . Give an informal argument that outlines the intuition behind the algorithm used by M justifies your answer. [4 points] . Solution: 1. The Turing Machine is M = ( Q, , ,,q ,q acc ,q rej ) where Q = { q ,q 1 ,q 2 ,q 3 ,q 4 ,q acc ,q rej ), = { a,b } , = { a,b, t ,X,Y } , 1 is given as follows ( q , t ) = ( q acc , t , R ) ( q ,a ) = ( q 2 ,X, R ) ( q ,b ) = ( q 3 ,X, R ) ( q 1 ,Y ) = ( q 1 ,Y, R ) ( q 1 ,a ) = ( q...
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This note was uploaded on 10/04/2011 for the course CS 373 taught by Professor Viswanathan,m during the Fall '08 term at University of Illinois, Urbana Champaign.

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cs373 fa10 hw6sol - Solutions for Problem Set 6 CS 373:...

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