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cs373 fa10 hw6sol

# 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 Σ = { 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, Σ , Γ ,δ,q ,q acc ,q rej ) where • Q = { q ,q 1 ,q 2 ,q 3 ,q 4 ,q acc ,q rej ), • Σ = { a,b } , • Γ = { a,b, t ,X,Y } , 1 • δ is given as follows δ ( q , t ) = ( q acc , t , R ) δ ( q ,a ) = ( q 2 ,X, R ) δ ( q ,b ) = ( q 3 ,X, R ) δ ( q 1 ,Y ) = ( q 1 ,Y, R ) δ ( q 1 ,a ) = ( q...
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cs373 fa10 hw6sol - Solutions for Problem Set 6 CS 373...

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