Skew and Infinitary Formal Power Series

  • Manfred Droste
  • Dietrich Kuske
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)


We investigate finite-state systems with costs. Departing from classical theory, in this paper the cost of an action does not only depend on the state of the system, but also on the time when it is executed. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger.

Using the previous results, we also deal with nonterminating behaviors and their costs. This includes an extension of the Büchi-acceptance condition from finite automata to weighted automata and provides a characterization of these nonterminating behaviors in terms of ω-rational formal power series. This generalizes a classical theorem of Büchi.


Formal Power Series Finite Automaton Discrete Event System Regular Word Weighted Automaton 
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 2003

Authors and Affiliations

  • Manfred Droste
    • 1
  • Dietrich Kuske
    • 1
  1. 1.Institut für AlgebraTechnische Universität DresdenDresdenGermany

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