We study a quantitative model of traces, i.e. trace series which assign to every trace an element from a semiring. We show the coincidence of recognizable trace series with those which are definable by restricted formulas from a weighted logics over traces. We use a translation technique from formulas over words to those over traces, and vice versa. This way, we show also the equivalence of aperiodic and first-order definable trace series.


Formal Power Series Atomic Formula Propositional Formula Trace Series Word Language 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ingmar Meinecke
    • 1
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany

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