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ICALP
2005
Springer

Weighted Automata and Weighted Logics

8 years 11 months ago
Weighted Automata and Weighted Logics
Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speech-to-text processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize B¨uchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted first-order logic and show that aperiodic series coincide with the first-order definable ones, if the semiring is locally finite, commutative and has some aperiodicity property.
Manfred Droste, Paul Gastin
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where ICALP
Authors Manfred Droste, Paul Gastin
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