**Unformatted text preview: **A TM or w = 1 y for some y ∈ A TM } . In other words, J is the union of all strings in A TM with a 0 appended in front of them, and all strings in A TM with a 1 appended in front of them. Show that neither J nor J is Turing-recognizable. Problem 4 Show that the Post Correspondence Problem (PCP) over a binary alphabet (i.e. over the alphabet Σ = { , 1 } ) is undecidable. Hint: Give a reduction from PCP over an arbitrary alphabet to PCP over a binary alphabet. You may use the fact that PCP over an arbitrary alphabet is undecidable....

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- Fall '07
- CharikarandChazelle
- Computer Science, Logic, Computational complexity theory, Turing reduction, Many-one reduction, Log-space reduction