Weighted automata and weighted logics with discounting

  • Authors:
  • Manfred Droste;George Rahonis

  • Affiliations:
  • Institute of Computer Science, Leipzig University, D-04009 Leipzig, Germany;Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

We introduce a weighted logic with discounting and we establish the Buchi-Elgot theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate Buchi and Muller automata with discounting over the max-plus and the min-plus semiring. We show their expressive equivalence with weighted MSO-sentences with discounting. In this case our logic has a purely syntactic definition. For the finite case, we obtain a purely syntactically defined weighted logic if the underlying semiring is additively locally finite.