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# assign4 - A ≤ m 1 5(25 Let J = w | either w = x for some...

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CS5371 Theory of Computation Homework 4 Due: 3:20 pm, December 21, 2007 (before class) 1. (20%) Let T = {h M i | M is a TM that accepts w R whenever it accepts w } . Show that T is undecidable. 2. (15%) In the silly Post Correspondence Problem , SPCP , in each pair the top string has the same length as the bottom string. Show that SPCP is decidable. 3. (20%) Show that A is Turing-recognizable if and only if A m A TM . 4. (20%) Show that A is decidable if and only if
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Unformatted text preview: A ≤ m * 1 * . 5. (25%) Let J = { w | either w = x for some x ∈ A TM , or w = 1 y for some y / ∈ A TM } . Show that A TM ≤ m J and A TM ≤ m ¯ J . Conclude that J and ¯ J are non-Turing-recognizable. 6. (Further studies: No marks) Let K = {h M i | M is a TM and L ( M ) = {h M i}} . Show that neither K nor the complement of K is Turing-recognizable. 1...
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