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Rational transductions and complexity of counting problems

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Abstract

This work presents an algebraic method, based on rational transductions, to study the sequential and parallel complexity of counting problems for regular and context-free languages. This approach allows us to obtain old and new results on the complexity of ranking and unranking as well as on other problems concerning the number of prefixes, suffixes, subwords, and factors of a word which belongs to a fixed language. Other results concern a suboptimal compression of finitely ambiguous context-free languages, the complexity of the value problem for rational and algebraic formal series in noncommuting variables, and a characterization of regular and Z-algebraic languages by means of ranking functions.

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Authors and Affiliations

  1. Laboratoire d'Informatique Théorique et de Programmation, Université Paris VII, UA248, Tour 55–56, 2 Place Jussieu, 75221, Paris Cedex 05, France

    C. Choffrut

  2. Dipartimento di Scienze dell'Informazione, Universitá degli Studi di Milano, via Comelico 39, 20135, Milano, Italy

    M. Goldwurm

Authors
  1. C. Choffrut
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  2. M. Goldwurm
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Additional information

A preliminary version of this work was accepted for presentation at the 17th Symposium on Mathematical Foundations of Computer Science (MFCS'92), Prague, August 24–28, 1992. This research was supported by ESPRIT Working Group ASMICS (CEC Contract No. 3166), PRC Mathématiques et Informatique, MURST Project 40% “Algoritmi, modelli di calcolo e strutture informative.”

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Choffrut, C., Goldwurm, M. Rational transductions and complexity of counting problems. Math. Systems Theory 28, 437–450 (1995). https://doi.org/10.1007/BF01185866

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  • DOI: https://doi.org/10.1007/BF01185866

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