Semirings, automata, languages
Semirings, automata, languages
The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
Competitive Markov decision processes
Competitive Markov decision processes
Journal of the ACM (JACM)
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
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
ACM Transactions on Computational Logic (TOCL)
Determinization of weighted finite automata over strong bimonoids
Information Sciences: an International Journal
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
Mean-payoff automaton expressions
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
Max and sum semantics for alternating weighted automata
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
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
Weighted automata and weighted MSO logics for average and long-time behaviors
Information and Computation
From model checking to model measuring
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
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Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights. We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata. For quantitative languages L1 and L2, we consider the pointwise operations max(L1, L2), min(L1, L2), 1 - L1, and the sum L1 + L2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations. We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism. Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.