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# hw7 - University of Central Florida School of Computer...

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University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof. Rene Peralta Homework 7 Due date: April 19 1. The following is a hierarchy of subsets of IN . regular CFL recursive re. P ( IN ) Show that the hierarchy is proper by giving examples of sets contained in each level but not in the next one. 2. In this question, let M be a Turing machine which takes as input a positive integer i and outputs (if it halts) a positive integer M ( i ). Denote by L M the language { M ( i ) | i = 1 , 2 , 3 , . . . } . Answer True or False (no need to justify your answer, do so at your own peril). Score is +1 for correct answer, -1 for incorrect answer. (a) It is always true that the language L M is recursive. (b) The set of languages over { 0 , 1 } recognized by C programs is countable. (c) There exists a language recognized by M but not recognized by any Finite Automaton. (d) Let H be the language composed of Turing machine represen- tations which halt iff the input is an even number. Then H is computable in polynomial time.

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