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Solved-Problem Set 5 -Solution

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Problem 1. (10 points) (3 points) A 2-stack PDA is a PDA with two stacks; its input tape is 1-way read only. Describe, at a high-level, a 2-stack PDA to recognize the language { : , ≥ 0}. (7 points) Can a 2-stack PDA recognize every Turing-recognizable language? Explain your reasoning. Problem 2. (10 points)…

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Problem 1. (10 points)

  1. (3 points) A 2-stack PDA is a PDA with two stacks; its input tape is 1-way read only. Describe, at a high-level, a 2-stack PDA to recognize the language { : , ≥ 0}.

  1. (7 points) Can a 2-stack PDA recognize every Turing-recognizable language? Explain your reasoning.

Problem 2. (10 points) Let = {〈 〉: ℎ }.

Show that is Turing-recognizable. Give a high-level description for your solution.

Problem 3. (10 points) Show that a language is decidable if and only if some enumerator enumerates the language in standard string order (lexicographically sorted in increasing length).

Problem 4. (10points) Show that every infinite TM-recognizable language has an infinite decidable subset.