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SIAM Journal on Control and Optimization
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The complexity of stochastic games
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Languages, automata, and logic
Handbook of formal languages, vol. 3
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Realizable and Unrealizable Specifications of Reactive Systems
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Memoryless determinacy of parity and mean payoff games: a simple proof
Theoretical Computer Science
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
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CONCUR 2005 - Concurrency Theory
Infinite Runs in Weighted Timed Automata with Energy Constraints
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
Better Quality in Synthesis through Quantitative Objectives
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Faster algorithms for mean-payoff games
Formal Methods in System Design
Measuring permissiveness in parity games: mean-payoff parity games revisited
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Parity games played on transition graphs of one-counter processes
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Half-Positional determinacy of infinite games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Bounded repairability of word languages
Journal of Computer and System Sciences
Solving parity games on integer vectors
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
A constraint-based approach to solving games on infinite graphs
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objectives. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP @? coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is logspace-equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP @? coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.