The Complexity of Request-Response Games
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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.
KeywordsMemory State Winning Strategy Linear Time Temporal Logic Winning Region Opposing Player
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- 3.Chatterjee, K., Henzinger, T., Horn, F.: Finitary winning in ω-regular games. ACM ToCL 11(1) (2009)Google Scholar
- 4.Dziembowski, S., Jurdziński, M., Walukiewicz, I.: How much memory is needed to win infinite games? In: Logic In Computer Science, pp. 99–110. IEEE Computer Society, Los Alamitos (1997)Google Scholar
- 5.Emerson, E., Jutla, C.: The complexity of tree automata and logics of programs. In: Foundations of Computer Science, pp. 328–337. IEEE Computer Society, Los Alamitos (1988)Google Scholar
- 7.Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190. ACM, New York (1989)Google Scholar