Extending Finite-Memory Determinacy by Boolean Combination of Winning Conditions

Authors Stéphane Le Roux, Arno Pauly, Mickael Randour

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Stéphane Le Roux
  • LSV, CNRS & ENS Cachan, Université Paris-Saclay, Cachan, France
Arno Pauly
  • Swansea University, Swansea, United Kingdom
Mickael Randour
  • F.R.S.-FNRS & UMONS - Université de Mons, Mons, Belgium

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Stéphane Le Roux, Arno Pauly, and Mickael Randour. Extending Finite-Memory Determinacy by Boolean Combination of Winning Conditions. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • games on graphs
  • finite-memory determinacy
  • multiple objectives


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