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International Symposium on Fundamentals of Computation Theory

FCT 1991: Fundamentals of Computation Theory pp 157–167Cite as

The complexity of computing maximal word functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 529))

Abstract

Maximal word functions occur in data retrival applications and have connections with ranking problems i.e. with problems related to data compression. Compute the maximal word function of a string x with respect to a language L ⊑ Σ* consists in determining the lexicographically greatest word belonging to L, which is smaller than or equal to x.

In this paper we investigate the complexity of computing maximal word functions, estabilishing sharp boundaries between classes of languages for which the maximal word function can be efficiently computed and classes of languages for which such a problem seems to be difficult to solve. For example, we will show that the maximal word function for the class of context free languages is in AC2 while for the class of languages accepted by 2-way pushdown automata the maximal word function can be efficiently (polynomially) computed if and only if P = NP. We will also show connections with ranking, detector and constructor functions as introduced in [14]. This paper is a continuation of the study enterprised by many authors ([6], [10], [13] and [14]) with the intention of identifying properties others than membership which are easily computable for certain class of languages.

Extended Abstract

Supported in part by MURST 40%

Supported in part by the ESPRIT Basic Research Action No. 3166: “Algebraic and Syntactic Methods in Computer Science (ASMICS).”

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Authors and Affiliations

  1. Dipartimento di Scienze dell'Informazione, Università degli Studi, Via Moretto da Brescia 9, 20133, Milano

    Danilo Bruschi & Giovanni Pighizzini

Authors
  1. Danilo Bruschi
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  2. Giovanni Pighizzini
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L. Budach

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© 1991 Springer-Verlag Berlin Heidelberg

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Bruschi, D., Pighizzini, G. (1991). The complexity of computing maximal word functions. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_60

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  • DOI: https://doi.org/10.1007/3-540-54458-5_60

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54458-6

  • Online ISBN: 978-3-540-38391-8

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