文章基本信息

标题：Graph Games on Ordinals
本地全文：下载
作者：Julien Cristau ; Florian Horn
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2008
卷号：2
页码：143-154
DOI：10.4230/LIPIcs.FSTTCS.2008.1748
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider an extension of Church\'s synthesis problem to ordinals by adding limit transitions to graph games. We consider game arenas where these limit transitions are defined using the sets of cofinal states. In a previous paper, we have shown that such games of ordinal length are determined and that the winner problem is \pspace-complete, for a subclass of arenas where the length of plays is always smaller than $\omega^\omega$. However, the proof uses a rather involved reduction to classical Muller games, and the resulting strategies need infinite memory. We adapt the LAR reduction to prove the determinacy in the general case, and to generate strategies with finite memory, using a reduction to games where the limit transitions are defined by priorities. We provide an algorithm for computing the winning regions of both players in these games, with a complexity similar to parity games. Its analysis yields three results: determinacy without hypothesis on the length of the plays, existence of memoryless strategies, and membership of the winner problem in \npconp.
关键词：Games; ordinals; zeno