The NP Search Problems of Frege and Extended Frege Proofs

Abstract

We study consistency search problems for Frege and extended Frege proofs&#8212;namely the NP search problems of finding syntactic errors in Frege and extended Frege proofs of contradictions. The input is a polynomial time function, or an oracle, describing a proof of a contradiction; the output is the location of a syntactic error in the proof. The consistency search problems for Frege and extended Frege systems are shown to be many-one complete for the provably total NP search problems of the second-order bounded arithmetic theories U<sup>1</sup><sub>2</sub> and V<sup>1</sup><sub>2</sub>, respectively.

DOI: 10.1145/3060145

Cite this paper

@article{Beckmann2017TheNS, title={The NP Search Problems of Frege and Extended Frege Proofs}, author={Arnold Beckmann and Samuel R. Buss}, journal={ACM Trans. Comput. Log.}, year={2017}, volume={18}, pages={11:1-11:19} }