Semirings, automata, languages
Semirings, automata, languages
Rational series and their languages
Rational series and their languages
Finite transition systems: semantics of communicating systems
Finite transition systems: semantics of communicating systems
Computer-aided verification of coordinating processes: the automata-theoretic approach
Computer-aided verification of coordinating processes: the automata-theoretic approach
Languages, automata, and logic
Handbook of formal languages, vol. 3
A design principles of a weighted finite-state transducer library
Theoretical Computer Science - Special issue on implementing automata
Symbolic Model Checking
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
On the Determinization of Weighted Finite Automata
SIAM Journal on Computing
Similarity Enrichment in Image Compression through Weighted Finite Automata
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Finite-state transducers in language and speech processing
Computational Linguistics
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Weighted tree automata and weighted logics
Theoretical Computer Science
Weighted automata and weighted logics
Theoretical Computer Science
Determinization of fuzzy automata with membership values in complete residuated lattices
Information Sciences: an International Journal
Theoretical Computer Science
Weighted Distributed Systems and Their Logics
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Deriving Syntax and Axioms for Quantitative Regular Behaviours
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Definable transductions and weighted logics for texts
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Quantitative Kleene coalgebras
Information and Computation
Weighted muller tree automata and weighted logics
Journal of Automata, Languages and Combinatorics
Łukasiewicz logic and weighted logics over MV-semirings
Journal of Automata, Languages and Combinatorics
MSO logics for weighted timed automata
Formal Methods in System Design
Max and sum semantics for alternating weighted automata
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Weighted picture automata and weighted logics
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Weighted automata and weighted logics on infinite words
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Weighted tree automata over valuation monoids and their characterization by weighted logics
Algebraic Foundations in Computer Science
Multi-Valued MSO Logics OverWords and Trees
Fundamenta Informaticae
Making weighted containment feasible: a heuristic based on simulation and abstraction
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Regular Functions and Cost Register Automata
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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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 Büchi’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.