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
Journal of the ACM (JACM)
Pushdown processes: games and model-checking
Information and Computation - Special issue on FLOC '96
Alternating-time temporal logic
Journal of the ACM (JACM)
How much memory is needed to win infinite games?
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Finitary winning in ω-regular games
ACM Transactions on Computational Logic (TOCL)
Symbolic synthesis of finite-state controllers for request-response specifications
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form "if a state with property Rq is visited, then later a state with property Rp is visited". The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-complete. We show that the problem becomes PSPACE-complete if we only consider games played on DAGs, and NP-complete or PTIME-complete if there is only one player (depending on whether he wants to enforce or spoil the request-response condition). We also present near-optimal bounds on the memory needed to design winning strategies for each player, in each case.