A multiparameter analysis of the boundedness problem for vector addition systems
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Supervisory control of a class of discrete event processes
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 mean payoff games on graphs
Theoretical Computer Science
Languages, automata, and logic
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Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Information and Computation
Alternating-time temporal logic
Journal of the ACM (JACM)
Interface Theories for Component-Based Design
EMSOFT '01 Proceedings of the First International Workshop on Embedded Software
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Better Quality in Synthesis through Quantitative Objectives
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Timed automata with observers under energy constraints
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ACM Transactions on Computational Logic (TOCL)
Reachability games on extended vector addition systems with states
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
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
Quantitative synthesis for concurrent programs
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Energy games in multiweighted automata
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
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
Theoretical Computer Science
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Antichain algorithms for finite automata
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Synthesis from LTL specifications with mean-payoff objectives
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Solving parity games on integer vectors
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Synthesis for multi-objective stochastic games: an application to autonomous urban driving
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω-regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on VASS (vector addition systems with states). Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.