COT5310F07FinalSamples - COT 5310 Fall 2006 More Sample...

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COT 5310 Fall 2006 More Sample Final Exam Questions Generally useful information. When I say a set S is re, unless I explicitly say otherwise, you may assume any of the following equivalent characterizations: 1. S is either empty or the range of a total recursive function f S . 2. S is the domain of a partial recursive function g S . If I say a function g is partially computable, then there is an index g (I know that’s overloading, but that’s okay as long as we understand each other), such that Φ g (x) = Φ (x, g) = g(x) . Here Φ is a universal partially recursive function. Moreover, there is a primitive recursive function STP , such that STP(x, g, t) is 1 (true), just in case g , started on x , halts in t or fewer steps. STP(x, g, t) is 0 (false), otherwise. Finally, there is another primitive recursive function VALUE , such that VALUE(x, g, t) is g(x) , whenever STP(x, g, t) . VALUE(x, g, t) is defined but meaningless if ~STP(x, g, t) . The notation f(x) means that f converges when computing with input x , but we don’t care about the value produced. In effect, this just means that x is in the domain of f . The notation f(x) means f diverges when computing with input x . In effect, this just means that x is not in the domain of f . The Post Correspondence problem is known to be undecidable. This problem is characterized by instances that are described by two n-ary sequences of non-empty words <x 1 ,x 2 ,…,x n >, <y 1 ,y 2 ,…,y n > . The question is whether or not there exists a sequence,
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This note was uploaded on 07/14/2011 for the course COT 5310 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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COT5310F07FinalSamples - COT 5310 Fall 2006 More Sample...

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