Borel determinacy of concurrent games

Authors:
Julian Gutierrez;Glynn Winskel
Affiliations:
Computer Science Department, University of Oxford, Oxford, UK;Computer Laboratory, University of Cambridge, Cambridge, UK
Venue:
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Year:
2013

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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.