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Complexity Classes as Mathematical Axioms

2008/09/30 by M. Freedman, Freedman, M.
Computer Science · Mathematics · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #cs.CC #math.GT

paper · pdf · doi:10.48550/arxiv.0810.0033

Some minor changes and one more reference. To appear in Ann. Math

arxiv created 2009/06/16 · arxiv updated 2009/12/01

Abstract

Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.

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