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Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra

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Abstract

It is well known that finite square matrices over a Kleene algebra again form a Kleene algebra. This is also true for infinite matrices under suitable restric- tions. One can use this fact to solve certain infinite systems of inequalities over a Kleene algebra. Automatic systems are a special class of infinite systems that can be viewed as infinite-state automata. Automatic systems can be collapsed us- ing Myhill-Nerode relations in much the same way that finite automata can. The Brzozowski derivative on an algebra of polynomials over a Kleene algebra gives rise to a triangular automatic system that can be solved using these methods. This provides an alternative method for proving the completeness of Kleene algebra.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853-7501, Ithaca, NY, USA

    Dexter Kozen

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  1. Dexter Kozen
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Kozen, D. (2001). Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_3

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  • DOI: https://doi.org/10.1007/3-540-44693-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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