组合迹的代数结构
Algebraic Structure of Combined Traces
摘要：
踪迹及其扩展（称为组合踪迹（comtrace））是用于并发系统分析和验证的两种形式模型。这两种模型都是基于起源于形式语言理论的概念，并且它们能够捕获系统操作过程中发生的原子行为的因果性和一致性的概念。本文的目的是将迹理论中一些成功的基本概念转移到迹的领域，并加以发展。特别是，我们介绍，然后应用的概念不可分割的步骤，字典的标准形式的comtrace，以及表示comtrace利用其线性投影到二进制动作subalphabets。我们还提供了两个算法相关的新概念。使用它们，可以有效地解决在comtrace的上下文中的步骤序列等价问题。人们可以把我们的结果看作是朝着发展无限组合痕迹以及可识别的组合痕迹语言迈出的第一步。
英文摘要：
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are able to capture the notions of causality and simultaneity of atomic actions which take place during the process of a system's operation. The aim of this paper is a transfer to the domain of comtraces and developing of some fundamental notions, which proved to be successful in the theory of traces. In particular, we introduce and then apply the notion of indivisible steps, the lexicographical canonical form of comtraces, as well as the representation of a comtrace utilising its linear projections to binary action subalphabets. We also provide two algorithms related to the new notions. Using them, one can solve, in an efficient way, the problem of step sequence equivalence in the context of comtraces. One may view our results as a first step towards the development of infinite combined traces, as well as recognisable languages of combined traces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
