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Tradeoffs between Nondeterminism and Complexity for Communication Protocols and Branching Programs

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

In this paper, lower bound and tradeoff results relating the computational power of determinism, nondeterminism, and randomness for communication protocols and branching programs are presented. The main results can be divided into the following three groups.

  1. (i)

    One of the few major open problems concerning nondeterministic communication complexity is to prove an asymptotically exact tradeoff between complexity and the number of available advice bits. This problem is solved here for the case of one-way communication.

  2. (ii)

    Multipartition protocols are introduced as a new type of communication protocols using a restricted form of non-obliviousness. In order to be able to study methods for proving lower bounds on multilective and/or non-oblivious computation, these protocols are allowed to either deterministically or nondeterministically choose between different partitions of the input. Here, the first results showing the potential increase of the computational power by non-obliviousness as well as boundaries on this power are derived.

  3. (iii)

    The above results (and others) are applied to obtain several new exponential lower bounds for different types of oblivious branching programs, which also yields new insights into the power of nondeterminism and randomness for the considered models. The proofs rely on a general technique described here which allows to prove explicit lower bounds on the size of oblivious branching programs in an easy and transparent way.

This work has been supported by DFG grants HR14/3-2 and We 1066/8-2.

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Author information

Authors and Affiliations

  1. Department of Computer Science I (Algorithms and Complexity), Technological University of Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Juraj Hromkovič

  2. Department of Computer Science, LS 2, University of Dortmund, 44221, Dortmund, Germany

    Martin Sauerhoff

Authors
  1. Juraj Hromkovič
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  2. Martin Sauerhoff
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Hromkovič, J., Sauerhoff, M. (2000). Tradeoffs between Nondeterminism and Complexity for Communication Protocols and Branching Programs. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_12

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  • DOI: https://doi.org/10.1007/3-540-46541-3_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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