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International Colloquium on Automata, Languages, and Programming

ICALP 1989: Automata, Languages and Programming pp 733–744Cite as

A combinatorial technique for separating counting complexity classes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 372))

Abstract

We introduce a new combinatorial technique to obtain relativized separations of certain complexity classes related to the idea of counting, like PP, G (exact counting), and ⊕P (parity). To demonstrate its usefulness we present three relativizations separating NP from G, NP from ⊕P and ⊕P from PP. Other separations follow from these results, and as a consequence we obtain an oracle separating PP from PSPACE, thus solving an open problem proposed by Angluin in [An,80]. From the relativized separations we obtain absolute separations for counting complexity classes with log-time bounded computation time.

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Author information

Authors and Affiliations

  1. Deptartamento L.S.I. (U.P.C), Pau Gargallo 5, 08028, Barcelona, Spain

    Jacobo Torán

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  1. Jacobo Torán
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Editor information

Giorgio Ausiello Mariangiola Dezani-Ciancaglini Simonetta Ronchi Della Rocca

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© 1989 Springer-Verlag Berlin Heidelberg

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Torán, J. (1989). A combinatorial technique for separating counting complexity classes. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035795

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  • DOI: https://doi.org/10.1007/BFb0035795

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51371-1

  • Online ISBN: 978-3-540-46201-9

  • eBook Packages: Springer Book Archive

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