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On complexity of counting

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Mathematical Foundations of Computer Science 1988 (MFCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 324))

Abstract

Let l, u: ℕ→ℕ, l<u. We give a full characterization of intervals [l, u] such that a polynomial-time ATM of a constant numer of alternations can verify the number of words of a given length and in a given (as its oracle) set A, provided that A's density function is in [l, u]. We prove also a new lower bound on the approximate counting: there is a recursive set A whose elements cannot be approximate counted in Σ p, A2 ∪ Π p, A2 .

This research was supported by the grant RP. I. 09 from the Institute of Informatics, University of Warsaw and the grant CPBP 01. 01 from the Institute of Mathematics, Polish Academy of Science.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51-151, Wrocław, Poland

    Marek Piotrow

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  1. Marek Piotrow
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Editor information

Michal P. Chytil Václav Koubek Ladislav Janiga

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© 1988 Springer-Verlag Berlin Heidelberg

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Piotrow, M. (1988). On complexity of counting. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017170

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  • DOI: https://doi.org/10.1007/BFb0017170

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50110-7

  • Online ISBN: 978-3-540-45926-2

  • eBook Packages: Springer Book Archive

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