Homework8 - C ={h M,k i | M is a TM which accepts some string of length k but M loops on some(other string of length k(Assume that the underlying

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ECS 120: Intoduction to the Theory of Computation Homework 8 Due: Friday, May 30, 2003 at the beginning of class Problem 1. Classify the following languages as decidable, recognizable (but not de- cidable), co-recognizable (but not decidable), or neither recognizable nor co- recognizable. Prove all your answers, giving decision procedures or reductions. A. L = {h M i | M accepts some even-length string } . B. L = {h M i | M accepts some palindrome } . C. L = {h M i | L ( M ) is Turing-decidable } . D. L = {h M i | L ( M ) is Turing-recognizable } . Problem 2. Show that the following language is not Turing-recognizable L
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Unformatted text preview: C = {h M,k i | M is a TM which accepts some string of length k but M loops on some (other) string of length k } . (Assume that the underlying alphabet has at least two characters.) Problem 3. Sipser Page 195, Problem 5.9. Problem 4. Sipser Page 195, Problem 5.13. Problem 5. Prove the following. A. 2 n is O ( n !) B. n ! is O (2 n 2 ) C. 2 n +100000000 is O (2 n ) Bonus. Show that the following language is not Turing-recognizable INFINITE TM = {h M i | M is a Turing machine and L ( M ) is inﬁnite } 1...
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This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.

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