进度度量，即时确定性，以及树形自动机的子集构造

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-06-22 DOI:10.1109/LICS.1992.185550

Nils Klarlund

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引用次数: 80

摘要

利用进度度量的概念，简化证明了M.O. Rabin(1969)的基本结论，即由树自动机定义的语言在互补下是封闭的。为了做到这一点，研究表明，对于基于树自动机的无限博弈，Y. Gurevich和L. Harrington(1982)的遗忘确定性可以被强化为根据Rabin接受条件试图获胜的玩家的即时确定性。并给出了这种接受条件的图论对偶定理。还提出了S. Safra(1988)确定结构的强化版本。综上所述，这些结果和Borel博弈的确定性产生了一种补充树自动机的直接方法。

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Progress measures, immediate determinacy, and a subset construction for tree automata

Using the concept of a progress measure, a simplified proof is given of M.O. Rabin's (1969) fundamental result that the languages defined by tree automata are closed under complementation. To do this, it is shown that for infinite games based on tree automata, the forgetful determinacy property of Y. Gurevich and L. Harrington (1982) can be strengthened to an immediate determinacy property for the player who is trying to win according to a Rabin acceptance condition. Moreover, a graph-theoretic duality theorem for such acceptance conditions is shown. Also presented is a strengthened version of S. Safra's (1988) determinization construction. Together these results and the determinacy of Borel games yield a straightforward method for complementing tree automata.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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