## Document Type

Article

## Publication Date

3-2011

## 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.

## Recommended Citation

Zhang, Liyu. "Proof system representations of degrees of disjoint NP-pairs." Information Processing Letters 111, no. 7 (2011): 348-351. https://doi.org/10.1016/j.ipl.2011.01.001

## Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

## Publication Title

Information Processing Letters

## DOI

10.1016/j.ipl.2011.01.001

## Comments

Original published version available at https://doi.org/10.1016/j.ipl.2011.01.001