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Lower bounds for randomized read-k-times branching programs

(Extended abstract)

  • Complexity I
  • Conference paper
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

Randomized branching programs are a probabilistic model of computation defined in analogy to the well-known probabilistic Turing machines. In this paper, we contribute to the complexity theory of randomized read-k-times branching programs.

We first consider the case read-k-times = 1 and present a function which has nondeterministic read-once branching programs of polynomial size, but for which every randomized read-once branching program with two-sided error at most 27/128 is exponentially large. The same function also exhibits an exponential gap between the randomized read-once branching program sizes for different constant worst-case errors, which shows that there is no “probability amplification” technique for read-once branching programs which allows to decrease the error to an arbitrarily small constant by iterating probabilistic computations.

Our second result is a lower bound for randomized read-k-times branching programs with two-sided error, where k > 1 is allowed. The bound is exponential for k < clog n, c an appropriate constant. Randomized read-k-times branching programs are thus one of the most general types of branching programs for which an exponential lower bound result could be established.

This work has been supported by DFG grants We 1066/7-3 and We 1066/8-1.

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Authors and Affiliations

  1. Fachbereich Informatik, Universität Dortmund, 44221, Dortmund, Germany

    Martin Sauerhoff

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  1. Martin Sauerhoff
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Sauerhoff, M. (1998). Lower bounds for randomized read-k-times branching programs. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028553

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  • DOI: https://doi.org/10.1007/BFb0028553

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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