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The Power of Counting

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Complexity Theory Retrospective

Abstract

In this overview, various applications and variations of counting in structural complexity theory are discussed. The ability of exact counting is shown to be closely related with the ability of nondeterministic complementation. Relations between counting classes and classes requiring unique or few accepting computations are revealed. Further, approximate counting and relativized results are discussed.

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Authors and Affiliations

  1. Abt. Theoretische Informatik, Universität Ulm, Postfach 4066, D-7900, Ulm, Germany

    Uwe Schöning

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  1. Uwe Schöning
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Editors and Affiliations

  1. College of Computer Science, Northeastern University, Boston, MA, 02115, USA

    Alan L. Selman

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Schöning, U. (1990). The Power of Counting. In: Selman, A.L. (eds) Complexity Theory Retrospective. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4478-3_9

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  • DOI: https://doi.org/10.1007/978-1-4612-4478-3_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8793-3

  • Online ISBN: 978-1-4612-4478-3

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