Proof system representations of degrees of disjoint NP-pairs

  • Zhang L
  • 3

    Readers

    Mendeley users who have this article in their library.
  • 0

    Citations

    Citations of this article.

Abstract

Let D be a set of many-one degrees of disjoint NP-pairs. We define a proof system representation of D to be a set of propositional proof systems P such that each degree in D contains the canonical NP-pair of a corresponding proof system in P and the degree structure of D is reflected by the simulation order among the corresponding proof systems in P. We also define a nesting representation of D to be a set of NP-pairs S such that each degree in D contains a representative NP-pair in S and the degree structure of D is reflected by the inclusion relations among their representative NP-pairs in S. We show that proof system and nesting representations both exist for D if the lower span of each degree in D overlaps with D on a finite set only. In particular, a linear chain of many-one degrees of NP-pairs has both a proof system representation and a nesting representation. This extends a result by Glaßer et al. (2009). We also show that in general D has a proof system representation if it has a nesting representation where all representative NP-pairs share the same set as their first components. © 2011 Elsevier B.V.

Author-supplied keywords

  • Canonical NP-pairs
  • Computational complexity
  • Degrees of disjoint NP-pairs
  • Propositional proof systems

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Liyu Zhang

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free