Rational series and their languages
Rational series and their languages
Handbook of theoretical computer science (vol. B)
Minimax algebra and applications
Fuzzy Sets and Systems
Finite Automata Computing Real Functions
SIAM Journal on Computing
An introduction to pseudo-linear algebra
Selected papers of the conference on Algorithmic complexity of algebraic and geometric models
Competitive Markov decision processes
Competitive Markov decision processes
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
The Kleene-Schützenberger theorem for formal power series in partially commuting variables
Information and Computation
A design principles of a weighted finite-state transducer library
Theoretical Computer Science - Special issue on implementing automata
Semirings, Automata and Languages
Semirings, Automata and Languages
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
Some Algorithmic Questions of Constructing Standard Bases
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Image and video coding with weighted finite automata
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
Finite-state transducers in language and speech processing
Computational Linguistics
Image texture analysis using weighted finite automata
Image texture analysis using weighted finite automata
On Aperiodic and Star-Free Formal Power Series in Partially Commuting Variables
Theory of Computing Systems
Fuzzy Sets and Systems
Skew and infinitary formal power series
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Kleene theorems for skew formal power series
Acta Cybernetica
Note: Schützenberger's theorem on formal power series follows from Kleene's theorem
Theoretical Computer Science
Weighted automata with discounting
Information Processing Letters
Probabilistic Weighted Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Cycle-Free Finite Automata in Partial Iterative Semirings
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Weighted automata and weighted logics with discounting
Theoretical Computer Science
Fuzzy regular languages over finite and infinite words
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
Regular expressions on average and in the long run
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Equational weighted tree transformations with discounting
Algebraic Foundations in Computer Science
Valuations of weighted automata: doing it in a rational way
Algebraic Foundations in Computer Science
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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We investigate finite-state systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are considered less urgent and carry less weight than close events. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger. Secondly, we deal with nonterminating behaviors and their weights. This includes an extension of the Büchi-acceptance condition from finite automata to weighted automata and provides a characterization of these nonterminating behaviors in terms of ω-rational formal power series. This generalizes a classical theorem of Büchi.