On the Existence of Complete Disjoint NP-Pairs

Abstract

Abstract-Disjoint NP-pairs are an interesting model of computation with important applications in cryptography and proof complexity. The question whether there exists a complete disjoint NP-pair was posed by Razborov in 1994 and is one of the most important problems in the field. In this paper we prove that there exists a complete disjoint NP-pair which is computed with access to a very weak oracle (a tally NP-oracle).In addition, we exhibit candidates for complete NP-pairs and apply our results to a recent line of research on the construction of hard tautologies from pseudorandom generators.

Do there exist complete sets for promise classes?

“…We thank the anonymous referees of both the journal and the conference versions of this paper for helpful comments and detailed suggestions on how to improve the paper. Preliminary versions of the results of this paper appeared as extended abstracts in the proceedings of the conferences CSR 2009 8 and SYNASC 2009 4. Research was supported in part by DFG grant KO 1053/5‐2.…”

Proof system representations of degrees of disjoint NP-pairs

“…We refer the reader to the survey by Glaßer et al [8] and recent literature [13,5,4,3,16] for more developments on the study of (canonical) disjoint NP-pairs.…”