Weighted automata with discounting

Authors:
Manfred Droste;Jacques Sakarovitch;Heiko Vogler
Affiliations:
Institute of Computer Science, Leipzig University, D-04009 Leipzig, Germany;LTCI, CNRS/ENST, École Nationale Supérieure des Télécommunications, F-75634 Paris Cedex, France;Faculty of Computer Science, Technische Universität Dresden, D-01062 Dresden, Germany
Venue:
Information Processing Letters
Year:
2008

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Abstract

We investigate weighted automata with discounting and their behaviors over semirings and finitely generated graded monoids. We characterize the discounted behaviors of weighted automata precisely as rational formal power series with a discounted form of the Cauchy product. This extends a classical result of Kleene-Schutzenberger. Here we show that the very special case of Schutzenberger's result for free monoids over singleton alphabets suffices to deduce our generalization.