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The complexity of the max word problem

and the power of one-way interactive proof systems

  • Complexity III
  • Conference paper
  • First Online:
STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

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Abstract

We study the complexity of the max word problem for matrices, a variation of the well-known word problem for matrices. We show that the problem is NP-complete, and cannot be approximated within any constant factor, unless P=NP. We describe applications of this result to probabilistic finite state automata, rational series and k-regular sequences. Our proof is novel in that it employs the theory of interactive proof systems, rather than a standard reduction argument. As another consequence of our results, we characterize NP exactly in terms of one-way interactive proof systems.

Work supported by NSF grant number CCR-8402565

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Wisconsin-Madison, USA

    Anne Condon

Authors
  1. Anne Condon
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Christian Choffrut Matthias Jantzen

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© 1991 Springer-Verlag Berlin Heidelberg

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Condon, A. (1991). The complexity of the max word problem. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020820

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  • DOI: https://doi.org/10.1007/BFb0020820

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

  • eBook Packages: Springer Book Archive

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