# day5 - How They relate Let S be an arbitrary subset of some...

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10/4/11 Dec 2, © UCF (Charles E. 11 How They relate Let S be an arbitrary subset of some universe U. The predicate χ S over U may be defined by: χ S(x) = true if and only if χ S is called the characteristic function of S. Let K be some arbitrary predicate defined over some universe U. The problem PK associated with K is the problem to decide of an arbitrary member x of U, whether or not K(x) is true. Let P be an arbitrary decision problem and let U denote the set of questions in P (usually just the set over which a single variable part of the questions ranges). The set SP associated with P is

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10/4/11 Dec 2, © UCF (Charles E. 22 Categorizing Problems (Sets) # 1 Recursively enumerable -- A set S is recursively enumerable (re) if S is empty (S = Ø) or there exists an algorithm F, over the natural numbers &, whose range is exactly S. A problem is said to be re if the set associated with it is re. Semi-Decidable
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day5 - How They relate Let S be an arbitrary subset of some...

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