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Equations Defining the Polynomial Closure of a Lattice of Regular Languages

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5556))

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Abstract

The polynomial closure Pol\((\mathcal{L})\) of a class of languages \(\mathcal{L}\) of A * is the set of languages that are finite unions of marked products of the form L 0 a 1 L 1 ... a n L n , where the a i are letters and the L i are elements of \(\mathcal{L}\).

The main result of this paper gives an equational description of Pol\((\mathcal{L})\), given an equational description of \(\mathcal{L}\), when \(\mathcal{L}\) is a lattice of regular languages closed under quotients, or a quotienting algebra of languages, as we call it in the sequel. The term “equational description” refers to a recent paper [5], where it was shown that any lattice of regular languages can be defined by a set of profinite equations. More formally, our main result can be stated as follows:

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Author information

Authors and Affiliations

  1. CAUL and Dep. Matemática da Faculdade de Ciências, Universidade de Lisboa Av., Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    Mário J. J. Branco

  2. LIAFA, Université Paris 7 and CNRS, Case 7014, 75205, Paris Cedex 13, France

    Jean-Éric Pin

Authors
  1. Mário J. J. Branco
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  2. Jean-Éric Pin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Tel Aviv University Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504, Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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Branco, M.J.J., Pin, JÉ. (2009). Equations Defining the Polynomial Closure of a Lattice of Regular Languages. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_10

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  • DOI: https://doi.org/10.1007/978-3-642-02930-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02929-5

  • Online ISBN: 978-3-642-02930-1

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