弱$ω$ -正则跟踪语言
Weak $ω$-Regular Trace Languages
摘要：
Mazurkiewicz迹描述了分布式系统的并发行为。跟踪封闭词语言，这是跟踪语言的“线性化”，构成了一个较弱的并发概念，但仍然给我们提供了工具来研究后者。在这方面，我们的贡献是双重的。首先，我们开发的定义，允许分类的$ω$ -定期跟踪语言在相应的跟踪封闭的$ω$ -定期字的语言，捕获E-可识别（可达性）和（确定性）Büchi可识别的语言。其次，我们证明了第一个自动机理论的结果，显示的等价性$ω$ -定期跟踪封闭的词语言和布尔组合的确定性$I$ -钻石Büchi可识别的跟踪封闭的语言。
英文摘要：
Mazurkiewicz traces describe concurrent behaviors of distributed systems. Trace-closed word languages, which are "linearizations" of trace languages, constitute a weaker notion of concurrency but still give us tools to investigate the latter. In this vein, our contribution is twofold. Firstly, we develop definitions that allow classification of $ω$-regular trace languages in terms of the corresponding trace-closed $ω$-regular word languages, capturing E-recognizable (reachability) and (deterministically) Büchi recognizable languages. Secondly, we demonstrate the first automata-theoretic result that shows the equivalence of $ω$-regular trace-closed word languages and Boolean combinations of deterministically $I$-diamond Büchi recognizable trace-closed languages.
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