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Solving Fixed-Point Equations by Derivation Tree Analysis

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Algebra and Coalgebra in Computer Science (CALCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6859))

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Abstract

Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the derivation trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.

This work was partially supported by the project “Polynomial Systems on Semirings: Foundations, Algorithms, Applications” of the Deutsche Forschungsgemeinschaft.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, 85748, Garching, Germany

    Javier Esparza & Michael Luttenberger

Authors
  1. Javier Esparza
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  2. Michael Luttenberger
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, 56127, Pisa, Italy

    Andrea Corradini

  2. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    Bartek Klin

  3. School of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Corina Cîrstea

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Esparza, J., Luttenberger, M. (2011). Solving Fixed-Point Equations by Derivation Tree Analysis. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-22944-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22943-5

  • Online ISBN: 978-3-642-22944-2

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