正则无限对策的前瞻度
Degrees of Lookahead in Regular Infinite Games
摘要：
我们研究的变种定期无限游戏，其中严格交替的两个球员之间的移动是受修改。第二个参与者可以将移动推迟有限步数，或者换句话说，在他的策略中利用对手移动的一些前瞻性。这捕获了分布式系统中的情况，例如，当通信中存在缓冲器时，或者当组件之间的信号传输延迟时。我们区分不同程度的前瞻战略，其中包括连续和有界前瞻战略。在第一种情况下，前视是有限的，可能是无限的大小，而在第二种情况下，它是有界的大小。我们证明了对于规则的无限对策，连续策略的可解性是可判定的，并且一个连续策略总是可以归结为一个有界前瞻策略。此外，这种前瞻性在识别获胜条件的给定奇偶自动机的大小上至多是双指数的。我们还表明，结果失败的非正规游戏，其中获胜的条件是由上下文无关的欧米茄语言。
英文摘要：
We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent. This captures situations in distributed systems, e.g. when buffers are present in communication or when signal transmission between components is deferred. We distinguish strategies with different degrees of lookahead, among them being the continuous and the bounded lookahead strategies. In the first case the lookahead is of finite possibly unbounded size, whereas in the second case it is of bounded size. We show that for regular infinite games the solvability by continuous strategies is decidable, and that a continuous strategy can always be reduced to one of bounded lookahead. Moreover, this lookahead is at most doubly exponential in the size of a given parity automaton recognizing the winning condition. We also show that the result fails for non-regular gamesxwhere the winning condition is given by a context-free omega-language.
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