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scan0021 - SDSU Spring 2006 CS—660 Combinatorial...

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Unformatted text preview: SDSU Spring 2006 CS—660 Combinatorial Algorithms 2.6% If A is a decision problem, then the complement of A ( denoted Ac ) is a decision problem such QxLl that every instance X of problem A is also an instance of problem Ac , and for every such instance X the decision A(X) for problem A is the logical complement (i.e., the negation) of the decision A°(X) for problem Ac . ( K For example, if the decision problem E is to decide whether the positive integer X is an even number, then the decision problem E'3 is to decide whether X is an odd number. 1 Q Or, if the decision problem PRIME is to decide whether the positive integer X is a prime S number, then the decision problem PRIMEc is to decide whether X is a composite (i.e., non-/ prime) number. 7 O Delm ition The set of decision problems co—P is defined as follows: co—P ={A| Ace P} That is, co—P is the set of all decision problems whose complements are in P . Definition The set of decision problems co—NP is defined as follows: co—NP ={A| Ace NP} That is, co—NP is the set of all decision problems whose complements are in NP . ...
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