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Expected Acceptance Counts for Finite Automata with Almost Uniform Input

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Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

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Abstract

If a sequence of independent unbiased random bits is fed into a finite automaton, it is straightforward to calculate the expected number of acceptances among the first n prefixes of the sequence. This paper deals with the situation in which the random bits are neither independent nor unbiased, but are nearly so. We show that, under suitable assumptions concerning the automaton, if the the difference between the entropy of the first n bits and n converges to a constant exponentially fast, then the change in the expected number of acceptances also converges to a constan texponentially fast. We illustrate this result with a variety of examples in which numbers folio wing the reciprocal distribution, whidi governs the significands of floating-point numbers, are recoded in the execution of various multiplication algorithms.

This research was supported by an NSERC Research Grant and a Canada Research Chair.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, 2366 Main Mall, Vancouver, V6T 1Z4, Canada

    Nie Holas Pippenger

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  1. Nie Holas Pippenger
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Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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Pippenger, N.H. (2002). Expected Acceptance Counts for Finite Automata with Almost Uniform Input. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_56

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  • DOI: https://doi.org/10.1007/3-540-36136-7_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

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