Weighted automata and weighted MSO logics for average and long-time behaviors
نویسندگان
چکیده
منابع مشابه
Weighted Timed MSO Logics
We aim to generalize Büchi’s fundamental theorem on the coincidence of recognizable and MSO-definable languages to a weighted timed setting. For this, we investigate subclasses of weighted timed automata and show how we can extend existing timed MSO logics with weights. Here, we focus on the class of weighted event-recording automata and define a weighted extension of the full logic MSOer(Σ) in...
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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...
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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...
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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 ...
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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...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2012
ISSN: 0890-5401
DOI: 10.1016/j.ic.2012.10.001