منابع مشابه
Weighted Automata and Weighted Logics
In automata theory, Büchi’s and Elgot’s fundamental theorems [6, 7, 25] established the coincidence of regular and ω-regular languages with languages definable in monadic second-order logic. At the same time, Schützenberger [57] investigated finite automata with weights and characterized their behaviours as rational formal power series. Both of these results have inspired a wealth of extensions...
متن کاملWeighted Automata and Weighted Logics with Discounting
We introduce a weighted logic with discounting and we establish Büchi’s and Elgot’s theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate Büchi 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 s...
متن کاملWeighted Picture Automata and Weighted Logics
The theory of two-dimensional languages, generalizing formal string languages, was motivated by problems arising from image processing and models of parallel computing. Weighted automata and series over pictures map pictures to some semiring and provide an extension to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will ...
متن کاملA Pebble Weighted Automata and Weighted Logics
We introduce new classes of weighted automata on words. Equipped with pebbles, they go beyond the class of recognizable formal power series: they capture weighted first-order logic enriched with a quantitative version of transitive closure. In contrast to previous work, this calculus allows for unrestricted use of existential and universal quantifications over positions of the input word. We ac...
متن کاملWeighted automata and weighted logics on innite words
We introduce weighted automata over in nite words with Muller acceptance condition and we show that their behaviors coincide with the semantics of weighted restricted MSO-sentences. Furthermore, we establish an equivalence property of weighted Muller and weighted Büchi automata over certain semirings. Keywords: Weighted logics, Weighted Muller automata, In nitary formal power series, Weighted B...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2007
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.02.055