Abstract
Just as traditional games can be represented by trees, so concurrent games can be represented by event structures. We show the determinacy of such concurrent games with Borel sets of configurations as winning conditions, provided they are race-free and bounded-concurrent. Both properties are shown necessary. The determinacy proof proceeds via a reduction to the determinacy of tree games, and the determinacy of these in turn reduces to the determinacy of Gale-Stewart games.
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References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)
Chatterjee, K., Henzinger, T.A.: A survey of stochastic ω-regular games. Journal of Computer and System Sciences 78(2), 394–413 (2012)
Clairambault, P., Gutierrez, J., Winskel, G.: The winning ways of concurrent games. In: LICS, pp. 235–244. IEEE Computer Society (2012)
Clairambault, P., Gutierrez, J., Winskel, G.: Imperfect information in logic and concurrent games. In: Coecke, B., Ong, L., Panangaden, P. (eds.) Abramsky Festschrift. LNCS, vol. 7860, pp. 7–20. Springer, Heidelberg (2013)
Gale, D., Stewart, F.: Infinite games with perfect information. Annals of Mathematical Studies 28, 245–266 (1953)
Martin, D.: Borel determinacy. Annals of Mathematics 102(2), 363–371 (1975)
Martin, D.: The determinacy of Blackwell games. Journal of Symbolic Logic 63(4), 1565–1581 (1998)
Nielsen, M., Plotkin, G., Winskel, G.: Petri nets, event structures and domains. Theoretical Computer Science 13, 85–108 (1981)
Nielsen, M., Winskel, G.: Models for concurrency. In: Handbook of Logic in Computer Science, pp. 1–148. Oxford University Press (1995)
Rideau, S., Winskel, G.: Concurrent strategies. In: LICS, pp. 409–418 (2011)
Winskel, G.: Prime algebraicity. Theoretical Computer Science 410(41), 4160–4168 (2009)
Zermelo, E.: On an application of set theory to the theory of the game of chess. In: Congress of Mathematicians, pp. 501–504. Cambridge University Press (1913)
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Gutierrez, J., Winskel, G. (2013). Borel Determinacy of Concurrent Games. In: D’Argenio, P.R., Melgratti, H. (eds) CONCUR 2013 – Concurrency Theory. CONCUR 2013. Lecture Notes in Computer Science, vol 8052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40184-8_36
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DOI: https://doi.org/10.1007/978-3-642-40184-8_36
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