answersH7 - University of Central Florida School of...

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University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof. Rene Peralta Homework 7: answers 1. The following is a hierarchy of subsets of IN . regular j CFL j recursive j re. j P ( IN ) Show that the hierarchy is proper by giving examples of sets contained in each level but not in the next one. answer: The question is poorly worded, apologies. But what I wanted was explained in class: 1 • { (2 n - 1)2 n - 1 | n 1 } is context-free but not regular. • { 2 n 2 | n 0 } is recursive but not context-free. Let C i be the i th C program in some canonical ordering. Then { 2 i 3 j | C i halts on input j } is recursively enumerable but not re- cursive; and { 2 i 3 j | C i loops on input j } is not recursively enu- merable. 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
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answersH7 - University of Central Florida School of...

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