Weighted Picture Automata and Weighted Logics

Mäurer, Ina

doi:10.1007/11672142_25

Cited by 22 publications

(15 citation statements)

References 11 publications

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“…The present paper shows the robustness of the weighted logic approach also for infinite words in the case of discounting. For weighted logics and automata on trees, pictures, traces, texts, distributed systems, and algebraic formal power series we refer the reader to [4,19,20,25,[38][39][40]42,45]. A preliminary version of this paper appeared as an extended abstract in the Proceedings of CIAA 2007 [17].…”

Section: Introductionmentioning

confidence: 99%

Weighted automata and weighted logics with discounting

Droste

Rahonis

2009

Theoretical Computer Science

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a b s t r a c tWe introduce a weighted logic with discounting and we establish the Büchi-Elgot 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 minplus 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.

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Section: Introductionmentioning

confidence: 99%

Weighted automata and weighted logics with discounting

Droste

Rahonis

2009

Theoretical Computer Science

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“…They prove that this fragment is expressively equivalent to weighted finite automata. Recently, this result has been generalized to weighted settings of infinite words [15], trees [16], pictures [21], traces [22], texts [19] and nested words [20].…”

Section: Introductionmentioning

confidence: 92%

“…In the setting of picture languages, Mäurer [21] introduces first-order step functions (rather than recognizable step functions as in [13]), and exploits the fact that every first-order definable picture language can be recognized by an unambiguous (rather than deterministic) picture automaton. The same approach is followed by Bollig and Meinecke [5] for Mazurkiewicz traces running over directed acyclic graphs.…”

Section: Introductionmentioning

confidence: 99%

MSO logics for weighted timed automata

Quaas

2011

Form Methods Syst Des

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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 weighted timed automata and show how we can extend Wilke's relative distance logic with weights taken from an arbitrary semiring. We show that every formula in our logic can effectively be transformed into a weighted timed automaton, and vice versa. The results indicate the robustness of weighted timed automata and may also be used for specification purposes.

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“…A logical characterization of weighted automata has been achieved only recently: Droste and Gastin opened a new research direction by providing a weighted MSO logic to define formal power series over words [7]. Their achievements have been extended, among others, to automata on infinite words [9], trees [10], pictures [16], and traces [17].…”

Section: Introductionmentioning

confidence: 99%

Weighted Distributed Systems and Their Logics

Bollig

Meinecke

2007

Logical Foundations of Computer Science

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Abstract. We provide a model of weighted distributed systems and give a logical characterization thereof. Distributed systems are represented as weighted asynchronous cellular automata. Running over directed acyclic graphs, Mazurkiewicz traces, or (lossy) message sequence charts, they allow for modeling several communication paradigms in a unifying framework, among them probabilistic sharedvariable and probabilistic lossy-channel systems. We show that any such system can be described by a weighted existential MSO formula and, vice versa, any formula gives rise to a weighted asynchronous cellular automaton.

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Weighted Picture Automata and Weighted Logics

Cited by 22 publications

References 11 publications

Weighted automata and weighted logics with discounting

Weighted automata and weighted logics with discounting

MSO logics for weighted timed automata

Weighted Distributed Systems and Their Logics

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