Probabilistic Weighted Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Determinization of weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Time for verification
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
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CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
An improved algorithm for determinization of weighted and fuzzy automata
Information Sciences: an International Journal
Regular expressions on average and in the long run
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Theoretical Computer Science
Weighted automata and multi-valued logics over arbitrary bounded lattices
Theoretical Computer Science
Weighted tree automata over valuation monoids and their characterization by weighted logics
Algebraic Foundations in Computer Science
Valuations of weighted automata: doing it in a rational way
Algebraic Foundations in Computer Science
A Kleene-Schützenberger Theorem for Trace Series over Bounded Lattices
Fundamenta Informaticae - Non-Classical Models of Automata and Applications II
Weighted automata and weighted MSO logics for average and long-time behaviors
Information and Computation
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be non-omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L1 and L2, we consider the operations max(L1, L2), min(L1, L2), and 1-L1, which generalize the boolean operations on languages, as well as the sum L1 + L2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.