Mazurkiewicz迹同时设置的环/级联积和相关分解结果（扩展版）
Wreath/cascade products and related decomposition results for the concurrent setting of Mazurkiewicz traces (extended version)
摘要：
我们开发了一个新的代数框架的原因Mazurkiewicz痕迹的语言。这个框架支持真正的并发性，并提供了一个非平凡的一般化的圈积操作的跟踪设置。建立了一种新的局部环积原理。新的框架是至关重要的，提出了可识别的痕迹语言，这是一个类似的Krohn-Rhodes定理的分解结果。我们证明了这种分解的结果在特殊情况下的非循环体系结构，并将其应用到扩展坎普定理到这种设置。我们还介绍和分析分布式自动机理论的操作称为本地和全球级联产品。最后，我们表明，非周期性的轨迹语言可以使用本地化和分布式的两个状态复位自动机的全球级联产品的特点。
英文摘要：
We develop a new algebraic framework to reason about languages of Mazurkiewicz traces. This framework supports true concurrency and provides a non-trivial generalization of the wreath product operation to the trace setting. A novel local wreath product principle has been established. The new framework is crucially used to propose a decomposition result for recognizable trace languages, which is an analogue of the Krohn-Rhodes theorem. We prove this decomposition result in the special case of acyclic architectures and apply it to extend Kamp's theorem to this setting. We also introduce and analyze distributed automata-theoretic operations called local and global cascade products. Finally, we show that aperiodic trace languages can be characterized using global cascade products of localized and distributed two-state reset automata.
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