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International Colloquium on Automata, Languages, and Programming

ICALP 1996: Automata, Languages and Programming pp 369–380Cite as

On type-2 probabilistic quantifiers

  • Session 8: Complexity Theory
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1099))

Abstract

We define and examine several probabilistic operators ranging over sets (i.e., operators of type 2), among others the formerly studied ALMOST-operator. We compare their power and prove that they all coincide for a wide variety of classes. As a consequence, we characterize the ALMOST-operator which ranges over infinite objects (sets) by a bounded-error probabilistic operator which ranges over strings, i.e. finite objects. This leads to a number of consequences about complexity classes of current interest. As applications, we obtain (a) a criterion for measure 1 inclusions of complexity classes, (b) a criterion for inclusions of complexity classes relative to a random oracle, (c) a new upper time bound for ALMOST-PSPACE, and (d) a characterization of ALMOST-PSPACE in terms of checking stack automata. Finally, a connection between the power of ALMOST-PSPACE and that of probabilistic NC1 circuits is given.

Research supported by NSF Grant CCR-93-02057, DFG Grant Wa 847/1, and a Feodor-Lynen-Fellowship from the Alexander von Humboldt Foundation. Research performed while the second and third author were visiting the Department of Mathematics, University of California, Santa Barbara.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Santa Barbara, 93106, Santa Barbara, CA, USA

    Ronald V. Book

  2. Lehrstuhl für Theoretische Informatik, Universität Würzburg, Am Exerzierplatz3, D-97072, Würzburg, Germany

    Heribert Vollmer & Klaus W. Wagner

Authors
  1. Ronald V. Book
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  2. Heribert Vollmer
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  3. Klaus W. Wagner
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Editor information

Friedhelm Meyer Burkhard Monien

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© 1996 Springer-Verlag Berlin Heidelberg

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Book, R.V., Vollmer, H., Wagner, K.W. (1996). On type-2 probabilistic quantifiers. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_143

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  • DOI: https://doi.org/10.1007/3-540-61440-0_143

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61440-1

  • Online ISBN: 978-3-540-68580-7

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