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arXiv · 2009.09802

On the Intrinsic Redundancy in Huge Natural Deduction proofs II: Analysing $M_{\imply}$ Super-Polynomial Proofs

Edward Hermann Haeusler
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Abstract

This article precisely defines huge proofs within the system of Natural Deduction for the Minimal implicational propositional logic \mil. This is what we call an unlimited family of super-polynomial proofs. We consider huge families of expanded normal form mapped proofs, a device to explicitly help to count the E-parts of a normal proof in an adequate way. Thus, we show that for almost all members of a super-polynomial family there at least one sub-proof or derivation of each of them that is repeated super-polynomially many times. This last property we call super-polynomial redundancy. Almost all, precisely means that there is a size of the conclusion of proofs that every proof with conclusion bigger than this size and that is huge is highly redundant too. This result points out to a refinement of compression methods previously presented and an alternative and simpler proof that CoNP=NP.

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Edward Hermann Haeusler. 2020-09-17. On the Intrinsic Redundancy in Huge Natural Deduction proofs II: Analysing $M_{\imply}$ Super-Polynomial Proofs. https://arxiv.org/abs/2009.09802

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