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arXiv · 1808.05791

Extending finite-memory determinacy by Boolean combination of winning conditions

Stéphane Le Roux·Arno Pauly·Mickael Randour
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Abstract

We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM strategies suffice to play optimally, even in a broad multi-objective setting. We show that our framework encompasses important classes of games from the literature, and permits to go further, using a unified approach. While such an approach cannot match ad-hoc proofs with regard to tightness of memory bounds, it has two advantages: first, it gives a widely-applicable criterion for FM determinacy; second, it helps to understand the cornerstones of FM determinacy, which are often hidden but common in proofs for specific (combinations of) winning conditions.

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Stéphane Le Roux, Arno Pauly, Mickael Randour. 2018-08-17. Extending finite-memory determinacy by Boolean combination of winning conditions. https://arxiv.org/abs/1808.05791

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