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# day25 - Exam#1 Review You are responsible for the style...

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Click to edit Master subtitle style 10/4/11 Exam#1 Review You are responsible for the first 196 pages of these notes, except for the P=NP material.

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 22 Sample Question#1 1. Present a register machine and a factor replacement system that each produce the value 1 (true), if x>y, and 0 (false), otherwise. a) For the register machine, assume it starts with x in R2 and y in R3, and all else 0. The result must end up in R1, with R2 and R3 unchanged. b) For the FRS, assume it starts with 3x5y
10/4/11 Dec 2, © UCF (Charles E. 33 Sample Question#2 2. Prove that the following are equivalent a) S is an infinite recursive (decidable) set. b) S is the range of a monotonically increasing total recursive function. Note: f is monotonically increasing means that Ex f(x+1) > f(x).

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 44 Sample Question#3 3. Let A and B be re sets. For each of the following, either prove that the set is re, or give a counterexample that results in some known non-re set.
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