Equational Aspects of a Parametric Family of Computational Problems and Consequences

Details Equational Aspects of a Parametric Family of Computational Problems and Consequences Equational Aspects of a Parametric Family of Computational Problems and Consequences

2004-09-21

arxiv.org/abs/cs/0409039v10

Computer Science

Computational Complexity

Scientific paper

In this paper, we introduce the SRXE problem as an instance of the following problem: "Given the equation E=0 and a member Ck of the parametric family of computational problems {Ck : k in N}, determine whether E=0 is solvable in a certain finite subset of the solution set of Ck". We show that SRXE is in NP and SRXE is decidable only if, with each instance, exhaustive search over a certain exponential set is performed. Consequently, SRXE is in NP - P and therefore, P is not NP.

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