The complexity of mean payoff games on graphs
Theoretical Computer Science
Metrics for Labeled Markov Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Probabilistic Finite-State Machines-Part I
IEEE Transactions on Pattern Analysis and Machine Intelligence
Weighted automata and weighted logics
Theoretical Computer Science
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Logical reliability of interacting real-time tasks
Proceedings of the conference on Design, automation and test in Europe
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
On Omega-Languages Defined by Mean-Payoff Conditions
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Expressiveness and Closure Properties for Quantitative Languages
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Handbook of Weighted Automata
Skew and infinitary formal power series
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Energy and mean-payoff games with imperfect information
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Church synthesis problem for noisy input
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Emptiness and universality problems in timed automata with positive frequency
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
The complexity of mean-payoff automaton expression
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A temporal logic with mean-payoff constraints
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.