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cs373 fa10 hw6

# cs373 fa10 hw6 - b R Y → Y R a → Y L a → a L b → b...

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Problem Set 6 CS 373: Theory of Computation Assigned: October 12, 2010 Due on: October 19, 2010 at 10am Instructions: This homework has two parts. The first part has practice problems from the textbook many of whose solutions can be found in the textbook itself; you must not turn in solutions for these. The second part has 3 problems that can be solved in groups of size at most 3. Please strictly follow the homework guidelines given on the class website; submitions not following these guidelines will not be graded. Recommended Reading: Lectures 13 and 14 and Chapter 3 of class textbook. Practice Problems Solve problems 3.1, 3.2, 3.3, 3.5, and 3.10. 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 0 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,

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Unformatted text preview: 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] . 1 Problem 2 . [Category: Design] For Σ = { B , # ,a,b } , design a Turing machine to recognize the language L = { B a 2 n # b n | n ≥ } Note: By deﬁnition B a # ∈ L . You need not prove that your construction is correct, but you must clearly explain the intuitions behind your construction. [10 points] Problem 3 . [Category: Comprehension+Proof] Solve problem 3.13. [10 points] 2...
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cs373 fa10 hw6 - b R Y → Y R a → Y L a → a L b → b...

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