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Partial Conway and Iteration Semiring-Semimodule Pairs

  • Zoltán Ésik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7020)

Abstract

A Conway semiring is a semiring S equipped with a unary operation *:S → S, called “star”, satisfying the sum star and product star identities. A Conway semiring-semimodule pair consists of a Conway semiring S and a left S-semimodule V together with a function ω : S → V, called “omega power”, subject to the sum omega and product omega identities. A Kleene type theorem holds in all Conway semiring-semimodule pairs that can be instantiated to give the equivalence of Büchi automata and regular languages over ω-words. However, sometimes the star and omega power operations cannot be defined in an appropriate manner on the whole semiring S. To handle this situation, we introduce partial Conway semiring-semimodule pairs and develop their basic theory in connection with automata. We prove a Kleene theorem, applicable to all partial Conway semiring-semimodule pairs.

Keywords

Matrix Theory Matricial Theory Regular Language Distinguished Ideal Rational Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Zoltán Ésik
    • 1
  1. 1.Dept. of Computer ScienceUniversity of SzegedHungary

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