Weighted grammars and Kleene's theorem
Information Processing Letters
Varieties of formal series on trees and Eilenberg's theorem
Information Processing Letters
Effective constructors the formal series of trees (French)
Theoretical Computer Science
Finite tree automata with cost functions
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Handbook of formal languages, vol. 3
Languages, automata, and logic
Handbook of formal languages, vol. 3
Positive tree representations and applications to tree automata
Information and Computation
The transducers and formal tree series
Acta Cybernetica
Information and Computation
Finiteness and Regularity in Semigroups and Formal Languages
Finiteness and Regularity in Semigroups and Formal Languages
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Towards more realistic (e.g., non-associative) “and”- and “or”-operations in fuzzy logic
Soft Computing - A Fusion of Foundations, Methodologies and Applications
A Kleene Theorem for Weighted Tree Automata
Theory of Computing Systems
Finitely presentable tree series
Acta Cybernetica
Weighted tree automata and weighted logics
Theoretical Computer Science
Weighted automata and weighted logics
Theoretical Computer Science
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids
Theory of Computing Systems
Weighted versus Probabilistic Logics
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Expressiveness and Closure Properties for Quantitative Languages
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Probabilistic Weighted Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Handbook of Weighted Automata
Fuzzy tree language recognizability
Fuzzy Sets and Systems
Tree acceptors and some of their applications
Journal of Computer and System Sciences
Recognizable tree series with discounting
Acta Cybernetica
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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
Weighted Logics for Unranked Tree Automata
Theory of Computing Systems
Weighted muller tree automata and weighted logics
Journal of Automata, Languages and Combinatorics
Models for quantitative distributed systems and multi-valued logics
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Deductive multi-valued model checking
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Weighted automata and weighted logics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Valuations of weighted automata: doing it in a rational way
Algebraic Foundations in Computer Science
Weighted automata and weighted MSO logics for average and long-time behaviors
Information and Computation
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Quantitative aspects of systems can be modeled by weighted automata. Here, we deal with such automata running on finite trees. Usually, transitions are weighted with elements of a semiring and the behavior of the automaton is obtained by multiplying the weights along a run. We turn to a more general cost model: the weight of a run is now determined by a global valuation function. An example of such a valuation function is the average of the weights. We establish a characterization of the behaviors of these weighted finite tree automata by fragments of weighted monadic second-order logic. For bi-locally finite bimonoids, we show that weighted tree automata capture the expressive power of several semantics of full weighted MSO logic. Decision procedures follow as consequences.