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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1994: STACS 94 pp 619–630Cite as

Automaticity: Properties of a measure of descriptional complexity

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

Abstract

Let σ and δ be nonempty alphabets with σ finite. Let f be a function mapping σ * to δ. We explore the notion of automaticity, which attempts to model how “close” f is to a finite-state function. Formally, the automaticity of f is a function Af(n) which counts the minimum number of states in any deterministic finite automaton that computes f correctly on all strings of length ≤n (and its behavior on longer strings is not specified). The same or similar notions were examined previously by Trakhtenbrot, Grinberg and Korshunov, Karp, Breitbart, Gabarró, Dwork and Stockmeyer, and Kaneps and Freivalds.

Research supported in part by NSERC.

Research supported in part by NSF grant #IRI-9221947.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Jeffrey Shallit

  2. Department of Computer Science, University of Kentucky, 40506, Lexington, KY, USA

    Yuri Breitbart

Authors
  1. Jeffrey Shallit
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  2. Yuri Breitbart
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Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Shallit, J., Breitbart, Y. (1994). Automaticity: Properties of a measure of descriptional complexity. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_176

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  • DOI: https://doi.org/10.1007/3-540-57785-8_176

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

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