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Gap-definability as a closure property

  • Stephen Fermer
  • Lance Fortnow
  • Lide Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

Gap-definability and the gap-closure operator were defined in [FFK91]. Few complexity classes were known at that time to be gap-definable. In this paper, we give simple characterizations of both gap-definability and the gap-closure operator, and we show that many complexity classes are gap-definable, including P#P, \(P^{\# P_{[1]} }\), PSPACE, EXP, NEXP, MP, and BP·⊕P. If a class is closed under union, intersection and contains λ and Σ*, then it is gap-definable if and only if it contains SPP; its gap-closure is the closure of this class together with SPP under union and intersection. On the other hand, we give some examples of classes which are reasonable gap-definable but not closed under union (resp. intersection, complement). Finally, we show that a complexity class such as PP or PSPACE, if it is not equal to SPP, contains a maximal proper gap-definable subclass which is closed under many-one reductions.

Keywords

Turing Machine Complexity Class GapP Function Closure Property Simple Characterization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Stephen Fermer
    • 1
  • Lance Fortnow
    • 2
  • Lide Li
    • 2
  1. 1.Computer Science DepartmentUniversity of Southern MainePortlandUSA
  2. 2.Department of Computer ScienceUniversity of ChicagoChicagoUSA

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