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
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Languages, automata, and logic
Handbook of formal languages, vol. 3
Alternating-time temporal logic
Journal of the ACM (JACM)
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Optimal Strategy Synthesis in Request-Response Games
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Formal Methods in System Design
Finitary winning in ω-regular games
ACM Transactions on Computational Logic (TOCL)
Faster algorithms for finitary games
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Promptness in w-regular automata
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Recurrence and transience for finite probabilistic tables
Theoretical Computer Science
Quantitatively fair scheduling
Theoretical Computer Science
Equilibria in quantitative reachability games
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Subgame perfection for equilibria in quantitative reachability games
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Code aware resource management
Formal Methods in System Design
On Equilibria in Quantitative Games with Reachability/Safety Objectives
Theory of Computing Systems
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Games on graphs with ω-regular objectives provide a model for the control and synthesis of reactive systems. Every ω-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Büchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett (fairness) objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.