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Graph games of infinite length provide a natural model for open reactive systems: one player (Eve) represents the controller and the other player (Adam) represents the environment. The evolution of the system depends on the decisions of both players. The specification for the system is usually given as an ω-regular language L over paths and Eve’s goal is to ensure that the play belongs to L irrespective of Adam’s behaviour.
The classical notion of winning strategies fails to capture several interesting scenarios. For example, strong fairness (Streett) conditions are specified by a number of request-grant pairs and require every pair that is requested infinitely often to be granted infinitely often: Eve might win just by preventing Adam from making any new request, but a “better” strategy would allow Adam to make as many requests as possible and still ensure fairness.
To address such questions, we introduce the notion of obliging games, where Eve has to ensure a strong condition Φ, while always allowing Adam to satisfy a weak condition Ψ. We present a linear time reduction of obliging games with two Muller conditions Φ and Ψ to classical Muller games. We consider obliging Streett games and show they are co-NP complete, and show a natural quantitative optimisation problem for obliging Streett games is in FNP. We also show how obliging games can provide new and interesting semantics for multi-player games.
KeywordsNash Equilibrium Weak Condition Winning Strategy Memory Content Classical Game
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- [BL69]Büchi, J.R., Landweber, L.H.: Solving Sequential Conditions by Finite-State Strategies. Transactions of the AMS 138, 295–311 (1969)Google Scholar
- [Chu62]Church, A.: Logic, arithmetic, and automata. In: Proceedings of the International Congress of Mathematicians, pp. 23–35 (1962)Google Scholar
- [DJW97]Dziembowski, S., Jurdziński, M., Walukiewicz, I.: How Much Memory is Needed to Win Infinite Games? In: Proceedings of LICS, pp. 99–110. IEEE, Los Alamitos (1997)Google Scholar
- [EJ88]Emerson, E.A., Jutla, C.S.: The Complexity of Tree Automata and Logics of Programs. In: Proceedings of FOCS, pp. 328–337. IEEE, Los Alamitos (1988)Google Scholar
- [PR89]Pnueli, A., Rosner, R.: On the Synthesis of a Reactive Module. In: Proceedings of POPL, pp. 179–190. ACM, New York (1989)Google Scholar
- [Sti01]Stirling, C.: Modal and Temporal Properties of Processes. Graduate Texts in Computer Science. Springer, Heidelberg (2001)Google Scholar
- [Tho97]Thomas, W.: Languages, Automata, and Logic. In: Handbook of Formal Languages. Beyond Words, vol. 3, ch. 7, pp. 389–455. Springer, Heidelberg (1997)Google Scholar