Weighted Automata and Weighted Logics with Discounting

We introduce a weighted logic with discounting and we establish B¨uchi’s and Elgot’s theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate B¨uchi 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.

• Type: Conference
• Year: 2007
• Where: WIA
• Authors: Manfred Droste, George Rahonis
• Keywords: Artificial Intelligence, Discounting, Weighted Automata, Weighted Logic, WIA 2007