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Distance automata having large finite distance or finite ambiguity

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Abstract

A distance automaton is a (nondeterministic finite) automaton which is equipped with a nonnegative cost function on its transitions. The distance of a word recognized by such a machine quantifies the expenses associated with the recognition of this word. The distance of a distance automaton is the maximal distance of a word recognized by this machine or is infinite, depending on whether or not a maximum exists. We present distance automata havingn states and distance 2n − 2. As a by-product we obtain regular languages having exponential finite order. Given a finitely ambiguous distance automaton withn states, we show that either its distance is at most 3n − 1, or the growth of the distance in this machine is linear in the input length. The infinite distance problem for these distance automata is NP-hard and solvable in polynomial space. The infinite-order problem for regular languages is PSPACE-complete.

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Authors and Affiliations

  1. Fachbereich Informatik, Johann Wolfgang Goethe-Universität, Frankfurt am Main 11, Postfach 111 932, W-6000, Federal Republic of Germany

    Andreas Weber

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  1. Andreas Weber
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A preliminary version of this article appeared in theProceedings of the 15th Symposium on Mathematical Foundations of Computer Science, 1990.

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Weber, A. Distance automata having large finite distance or finite ambiguity. Math. Systems Theory 26, 169–185 (1993). https://doi.org/10.1007/BF01202281

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  • DOI: https://doi.org/10.1007/BF01202281

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