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# hw6_1 - w Prove that L is decidable Hint you should be able...

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Finite Automata and Theory of Computation October 18, 2007 Handout 13: Homework 6 Professor: Moses Liskov Due: October 25, 2007, in class. Problem 1 Prove that the class of Turing-recognizable languages is closed under concatenation and star. Problem 2 Prove that if an enumerator E produces the strings of L ( E ) in lexicographic order, then L ( E ) is decidable. Problem 3 Prove that if a language L is decidable, then there is an enumerator E such that E enu- merates L and produces the strings of L in lexicographic order. Problem 4 Let L = {h M, w i| M is a TM that moves left at some point during its computation on
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Unformatted text preview: w } . Prove that L is decidable. Hint: you should be able to detect if M loops forever without ever moving left. Problem 5 Let INFINITE DFA = {h M i| M is a DFA that accepts an inﬁnite language } . Prove that INFINITE DFA is decidable. Problem 6 (optional) A 2-stack PDA is simply a PDA with two separate stacks instead of one. Prove that the class of languages that can be recognized by 2-stack PDAs is the class of Turing-recognizable languages. 13-1...
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