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 Theory and Its Applications
Automata Theory and Its Applications
On the Determinization of Weighted Finite Automata
SIAM Journal on Computing
Finite-state transducers in language and speech processing
Computational Linguistics
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
Weighted tree automata and weighted logics
Theoretical Computer Science
On Aperiodic and Star-Free Formal Power Series in Partially Commuting Variables
Theory of Computing Systems
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
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Weighted automata and weighted logics on infinite words
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Determinization of fuzzy automata with membership values in complete residuated lattices
Information Sciences: an International Journal
Theoretical Computer Science
Weighted Logics for Nested Words and Algebraic Formal Power Series
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Better Quality in Synthesis through Quantitative Objectives
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
How to Tackle Integer Weighted Automata Positivity
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Weighted automata and weighted logics with discounting
Theoretical Computer Science
Weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Definable transductions and weighted logics for texts
Theoretical Computer Science
Myhill--Nerode type theory for fuzzy languages and automata
Fuzzy Sets and Systems
Recognizable tree series with discounting
Acta Cybernetica
Weighted automata and weighted logics with discounting
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
A Kleene-Schützenberger theorem for weighted timed automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
ACM Transactions on Computational Logic (TOCL)
Time for verification
Pebble weighted automata and transitive closure logics
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Describing average- and longtime-behavior by weighted MSO logics
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Energy and mean-payoff games with imperfect information
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Mean-payoff automaton expressions
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Finite automata theory with membership values in lattices
Information Sciences: an International Journal
Finite-state methods and models in natural language processing
Natural Language Engineering
On memoryless quantitative objectives
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Theoretical Computer Science
Weighted automata and multi-valued logics over arbitrary bounded lattices
Theoretical Computer Science
Measuring and synthesizing systems in probabilistic environments
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Weighted tree automata over valuation monoids and their characterization by weighted logics
Algebraic Foundations in Computer Science
The complexity of mean-payoff automaton expression
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Probabilistic automata and probabilistic logic
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Weighted automata and weighted MSO logics for average and long-time behaviors
Information and Computation
Weighted nested word automata and logics over strong bimonoids
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
A temporal logic with mean-payoff constraints
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
Weighted modal transition systems
Formal Methods in System Design
Quantitative Monadic Second-Order Logic
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 Buchi'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 particular sentences of 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.