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Distance automata having large finite distance or finite ambiguity

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Mathematical Foundations of Computer Science 1990 (MFCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 452))

Abstract

A distance automaton (DA) 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 DA is the maximal distance of a word recognized by this DA or is infinite, depending on whether or not a maximum exists. We present DA's having n states and distance 2n−2. We also show: Given a finitely ambiguous DA with n states, then either its distance is at most 3n−2, or the growth of the distance in this DA is linear in the input length. As a by-product of the first result we obtain regular languages having exponential finite order.

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Authors and Affiliations

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

    Andreas Weber

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  1. Andreas Weber
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Branislav Rovan

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© 1990 Springer-Verlag Berlin Heidelberg

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Weber, A. (1990). Distance automata having large finite distance or finite ambiguity. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029649

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  • DOI: https://doi.org/10.1007/BFb0029649

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52953-8

  • Online ISBN: 978-3-540-47185-1

  • eBook Packages: Springer Book Archive

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