Semirings and Formal Power Series

  • Manfred Droste
  • Werner Kuich
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)


This chapter presents basic foundations for the theory of weighted automata: semirings and formal power series. A fundamental question is how to extend the star operation (Kleene iteration) from languages to series. For this, we investigate ordered, complete and continuous semirings and the related concepts of star semirings and Conway semirings. We derive natural properties for the Kleene star of cycle-free series and also of matrices often used to analyze the behavior of weighted automata. Finally, we investigate cycle-free linear equations which provide a useful tool for proving identities for formal power series.


Power Series Formal Language Formal Power Series Automaton Theory Commutative Monoid 
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 2009

Authors and Affiliations

  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany
  2. 2.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienWienAustria

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