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Restrictive acceptance suffices for equivalence problems

  • Bernd Borchert
  • Lane A. Hemaspaandra
  • Jörg Rothe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach—weaker in strength of evidence but more broadly applicable—to suggesting that concrete NP problems are not NP-complete. In particular we introduce the class EP, the subclass of NP consisting of those languages accepted by NP machines that when they accept always have a number of accepting paths that is a power of two. Since if any NP-complete set is in EP then all NP sets are in EP, it follows—with whatever degree of strength one believes that EP differs from NP—that membership in EP can be viewed as evidence that a problem is not NP-complete.

We show that the negation equivalence problem for OBDDs (ordered binary decision diagrams [17,12]) and the interchange equivalence problem for 2-dags are in EP. We also show that for boolean negation [20] the equivalence problem is in EPNP, thus tightening the existing NPNP upper bound. We show that FewP [2], bounded ambiguity polynomial time, is contained in EP, a result that is not known to follow from the previous SPP upper bound. For the three problems and classes just mentioned with regard to EP, no proof of membership/containment in UP is known, and for the problem just mentioned with regard to EPNP, no proof of membership in UPNP is known. Thus, EP is indeed a tool that gives evidence against NP-completeness in natural cases where UP cannot currently be applied.

Keywords

Boolean Function Equivalence Problem Binary Decision Diagram Polynomial Hierarchy Order Binary Decision Diagram 
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 1999

Authors and Affiliations

  • Bernd Borchert
    • 1
  • Lane A. Hemaspaandra
    • 2
  • Jörg Rothe
    • 3
  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Dept. of Computer ScienceUniversity of RochesterRochesterUSA
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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