Partial orders are a fundamental mathematical structure capable of representing concurrency and causality on a set of atomic events. In many applications it is essential to consider multiple partial orders, each representing a particular behavioral scenario or an operating mode of a system. With the exploding growth of the complexity of systems that software and hardware engineers design today, it is no longer feasible to represent each partial order of a large system explicitly, therefore compressed representations of sets of partial orders become essential for improving the scalability of design automation tools. In this paper we study two well known mathematical formalisms capable of the compressed representation of sets of partial orders: Labeled Event Structures and Conditional Partial Order Graphs. We discuss their advantages and disadvantages and propose efficient algorithms for transforming a set of partial orders from a given compressed representation in one formalism into an equivalent representation in another formalism without explicitly enumerating every partial order. The proposed algorithms make use of an intermediate mathematical formalism which we call Conditional Labeled Event Structures that combines the advantages of both structures. Finally, we compare these structures on a number of benchmarks coming from concurrent software and hardware domains.

中文翻译：

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并发系统的紧凑且可有效验证的模型

偏序是一种基本的数学结构，能够表示一组原子事件的并发性和因果关系。在许多应用中，必须考虑多个偏序，每个偏序代表一个特定的行为场景或系统的操作模式。随着当今软件和硬件工程师设计的系统复杂性的爆炸式增长，明确表示大型系统的每个偏序已不再可行，因此对偏序集的压缩表示对于提高设计自动化的可扩展性变得必不可少工具。在本文中，我们研究了两种众所周知的能够压缩表示偏序集的数学形式：标记事件结构和条件偏序图。我们讨论了它们的优点和缺点，并提出了有效的算法，用于将一组偏序从一种形式主义中的给定压缩表示转换为另一种形式主义中的等效表示，而无需明确枚举每个偏序。所提出的算法利用了一种中间数学形式，我们称之为条件标记事件结构，它结合了两种结构的优点。最后，我们在来自并发软件和硬件领域的许多基准测试中比较了这些结构。所提出的算法利用了一种中间数学形式，我们称之为条件标记事件结构，它结合了两种结构的优点。最后，我们在来自并发软件和硬件领域的许多基准测试中比较了这些结构。所提出的算法利用了一种中间数学形式，我们称之为条件标记事件结构，它结合了两种结构的优点。最后，我们在来自并发软件和硬件领域的许多基准测试中比较了这些结构。