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Restrictive acceptance suffices for equivalence problems

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Book cover Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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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.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Heidelberg, 69120, Heidelberg, Germany

    Bernd Borchert

  2. Dept. of Computer Science, University of Rochester, Rochester, NY, 14627, USA

    Lane A. Hemaspaandra

  3. Institut für Informatik, Friedrich-Schiller-Universität Jena, 07740, Jena, Germany

    Jörg Rothe

Authors
  1. Bernd Borchert
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  2. Lane A. Hemaspaandra
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  3. Jörg Rothe
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Borchert, B., Hemaspaandra, L.A., Rothe, J. (1999). Restrictive acceptance suffices for equivalence problems. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_9

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  • DOI: https://doi.org/10.1007/3-540-48321-7_9

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  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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