Multi-buffer simulation is an extension of simulation preorder that can be used to approximate inclusion of languages recognised by Büchi automata up to their trace closures. DUPLICATOR can use some bounded or unbounded buffers to simulate SPOILER’s move. It has been shown that multi-buffer simulation can be characterised with the existence of a continuous function. In this paper, we show that such a characterisation can be refined to a more restricted case, that is, to the one where DUPLICATOR only uses bounded buffers, by requiring the function to be Lipschitz continuous instead of only continuous. This characterisation however only holds for some restricted classes of automata. One of the automata should only produce words where each letter cannot commute unboundedly. We show that this property can be syntactically characterised with cyclic-path-connectedness, a refinement of syntactic condition on automata that have regular trace closure. We further show that checking cyclic-path-connectedness is indeed co-NP-complete.

中文翻译：

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多缓冲区仿真的拓扑表征

多缓冲区模拟是模拟预排序的扩展，可用于近似估计Büchi自动机识别的语言，直至其跟踪闭包为止。DUPLICATOR可以使用一些有界或无界缓冲区来模拟SPOILER的移动。已经表明，可以通过连续函数的存在来表征多缓冲区仿真。在本文中，我们表明，通过要求函数是Lipschitz连续的而不是连续的，可以将这种表征改进到更严格的情况，即DUPLICATOR仅使用有界缓冲区的情况。但是，此特征仅适用于某些受限类别的自动机。自动机之一只能产生每个字母不能无限制通勤的单词。我们表明，此属性可以用循环路径连接来进行句法表征，这是对具有规则迹线闭合的自动机上句法条件的改进。我们进一步表明，检查循环路径的连通性确实是共NP完整的。