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标题：Parameterized complexity of games with monotonically ordered omega-regular objectives
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作者：V{\'e}ronique Bruy{\`e}re ; Quentin Hautem ; Jean-Fran{\c{c}}ois Raskin 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：118
页码：1-16
DOI：10.4230/LIPIcs.CONCUR.2018.29
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are satisfied against any behavior of Player 2. When this is not possible to satisfy all the objectives at once, an alternative is to use some preorder on the objectives according to which subset of objectives Player 1 wants to satisfy. For example, it is often natural to provide more significance to one objective over another, a situation that can be modelled with lexicographically ordered objectives for instance. Inspired by recent work on concurrent games with multiple omega-regular objectives by Bouyer et al., we investigate in detail turned-based games with monotonically ordered and omega-regular objectives. We study the threshold problem which asks whether player 1 can ensure a payoff greater than or equal to a given threshold w.r.t. a given monotonic preorder. As the number of objectives is usually much smaller than the size of the game graph, we provide a parametric complexity analysis and we show that our threshold problem is in FPT for all monotonic preorders and all classical types of omega-regular objectives. We also provide polynomial time algorithms for Büchi, coBüchi and explicit Muller objectives for a large subclass of monotonic preorders that includes among others the lexicographic preorder. In the particular case of lexicographic preorder, we also study the complexity of computing the values and the memory requirements of optimal strategies.
关键词：two-player zero-sum games played on graphs; omega-regular objectives; ordered objectives; parameterized complexity