Detecting cycles in dynamic graphs in polynomial time
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
The complexity of mean payoff games on graphs
Theoretical Computer Science
The Emptiness Problem for Intersections of Regular Languages
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Weighted automata and weighted logics
Theoretical Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Logical reliability of interacting real-time tasks
Proceedings of the conference on Design, automation and test in Europe
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
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
ACM Transactions on Computational Logic (TOCL)
Mean-payoff automaton expressions
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
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
Temporal Specifications with Accumulative Values
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Weighted automata and weighted logics on infinite words
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Automated analysis of real-time scheduling using graph games
Proceedings of the 16th international conference on Hybrid systems: computation and control
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Quantitative languages are extension of Boolean languages that assign to each word a real number. With quantitative languages, systems and specifications can be formalized more accurately. For example, a system may use a varying amount of some resource (e.g., memory consumption, or power consumption) depending on its behavior, and a specification may assign a maximal amount of available resource to each behavior, or fix the long-run average available use of the resource. 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. Mean-payoff automata forms a class of quantitative languages that is not robust, since it is not closed under the basic algebraic operations: min, max, sum and numerical complement. The class of mean-payoff automaton expressions, recently introduced by Chatterjee et al., is currently the only known class of quantitative languages that is robust, expressive and decidable. This class is defined as the closure of mean-payoff automata under the basic algebraic operations. In this work, we prove that all the classical decision problems for mean-payoff expressions are PSPACE-complete. Our proof improves the previously known 4EXPTIME upper bound. In addition, our proof is significantly simpler, and fully accessible to the automata-theoretic community.