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On the power of generalized Mod-classes

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Abstract

We investigate the computational power of the new counting class ModP which generalizes the classes Mod p P,p prime. We show that ModP is polynomialtime truth-table equivalent in power to #P and that ModP is contained in the class AmpMP. As a consequence, the classes PP, ModP, and AmpMP are all Turing equivalent, and thus AmpMP and ModP are not low for MP unless the counting hierarchy collapses to MP. Furthermore, we show that every set in C=P is reducible to some set in ModP via a random many-one reduction that uses only logarithmically many random bits. Hence, ModP and AmpMP are not closed under polynomial-time conjunctive reductions unless the counting hierarchy collapses.

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Authors and Affiliations

  1. Abteilung für Theoretische Informatik, Universität Ulm, Oberer Eselsberg, D-89069, Ulm, Germany

    J. Köbler

  2. Department of Mathematics, College of Humanities and Sciences, Nihon University, Sakurajyosui 3-25-40, Setagaya-ku, 156, Tokyo, Japan

    Seinosuke Toda

Authors
  1. J. Köbler
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  2. Seinosuke Toda
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The work of the second author was done in part while visiting the Fakultät für Informatik, Universität Ulm.

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Köbler, J., Toda, S. On the power of generalized Mod-classes. Math. Systems Theory 29, 33–46 (1996). https://doi.org/10.1007/BF01201812

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  • DOI: https://doi.org/10.1007/BF01201812

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