Finite Automata Computing Real Functions
SIAM Journal on Computing
The complexity of probabilistic verification
Journal of the ACM (JACM)
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Competitive Markov decision processes
Competitive Markov decision processes
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Recognizing ?-regular Languages with Probabilistic Automata
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Compositional Quantitative Reasoning
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Skew and infinitary formal power series
Theoretical Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Expressiveness and Closure Properties for Quantitative Languages
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
On decision problems for probabilistic Büchi automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Verifying quantitative properties using bound functions
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
Describing average- and longtime-behavior by weighted MSO logics
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Regular expressions on average and in the long run
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Language equivalence for probabilistic automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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
Compositional reasoning for markov decision processes
FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
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
Making weighted containment feasible: a heuristic based on simulation and abstraction
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
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Nondeterministic weighted automata are finite automata with numerical weights on transitions. They define quantitative languages L that assign to each word w a real number L (w ). The value of an infinite word w is computed as the maximal value of all runs over w , and the value of a run as the supremum, limsup, liminf, limit average, or discounted sum of the transition weights. We introduce probabilistic weighted automata, in which the transitions are chosen in a randomized (rather than nondeterministic) fashion. Under almost-sure semantics (resp. positive semantics), the value of a word w is the largest real v such that the runs over w have value at least v with probability 1 (resp. positive probability). We study the classical questions of automata theory for probabilistic weighted automata: emptiness and universality, expressiveness, and closure under various operations on languages. For quantitative languages, emptiness and universality are defined as whether the value of some (resp. every) word exceeds a given threshold. We prove some of these questions to be decidable, and others undecidable. Regarding expressive power, we show that probabilities allow us to define a wide variety of new classes of quantitative languages, except for discounted-sum automata, where probabilistic choice is no more expressive than nondeterminism. Finally, we give an almost complete picture of the closure of various classes of probabilistic weighted automata for the following pointwise operations on quantitative languages: max, min, sum, and numerical complement.