On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the Logical Characterisation of Performability Properties
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Weighted automata and weighted logics
Theoretical Computer Science
The Satisfiability Problem for Probabilistic CTL
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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
Better Quality in Synthesis through Quantitative Objectives
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Mean-payoff automaton expressions
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Quantitative synthesis for concurrent programs
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Temporal Specifications with Accumulative Values
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Markov decision processes with multiple objectives
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Measuring and synthesizing systems in probabilistic environments
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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In the quantitative verification and synthesis of reactive systems, the states or transitions of a system are associated with payoffs, and a quantitative property of a behavior of the system is often characterized by the mean payoff for the behavior. This paper proposes an extension of LTL thatdescribes mean-payoff constraints. For each step of a behavior of a system, the payment depends on a system transition and a temporal property of the behavior. A mean-payoff constraint is a threshold condition for the limit supremum or limit infimum of the mean payoffs of a behavior. This extension allows us to describe specifications reflecting qualitative and quantitative requirements on long-run average of costs and the frequencies of satisfaction of temporal properties. Moreover, we develop an algorithm for the emptiness problems of multi-dimensional payoff automata with Büchi acceptance conditions and multi-threshold mean-payoff acceptance conditions. The emptiness problems are decided by solving linear constraint satisfaction problems, and the decision problems of our logic are reduced to the emptiness problems. Consequently, we obtain exponential-time algorithms for the model- and satisfiability-checking of the logic. Some optimization problems of the logic can also be reduced to linear programming problems.