hw5_1 - Finite Automata and Theory of Computation October 4...

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Unformatted text preview: Finite Automata and Theory of Computation October 4, 2007 Handout 11: Homework 5 Professor: Moses Liskov Due: October 18, 2007, in class. Problem 1 For each language, determine if that language is context-free or not, and prove your answer. (a) L 1 = { w | w = w R and w contains an equal number of 0s and 1s } . (b) L 2 = { a 1 b 2 c | a 6 = b or a 6 = c } . Problem 2 Prove that the language { #0 n #0 m #0 l # | l = mn } is Turing-recognizable by giving a detailed description of a Turing machine that accepts it, and proving that your construction works. Give your Turing machine as an algorithm. Problem 3 Prove that the language { #0 n # | n is a prime number } is Turing-recognizable by giving a description of a Turing machine that accepts it, and proving that your construction works. Give your Turing machine as an algorithm. Problem 4 A Turing machine with doubly-infinite tape is similar to an ordinary TM, except that there is no left edge of the tape. Initially, the head is positioned over the first symbol of the input;is no left edge of the tape....
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hw5_1 - Finite Automata and Theory of Computation October 4...

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