并发的几何模型与经典模型之间的形式化关系
Formal Relationships Between Geometrical and Classical Models for Concurrency
摘要：
在过去的几十年中，已经提出了各种各样的并发程序模型，每一个专注于计算的各个方面：跟踪等价性，事件之间的因果关系，冲突和时间表，由于资源访问等最近，模型与几何风味已被引入，基于立方集的概念。这些模型非常丰富和富有表现力，因为它们可以表示任何一组事件之间的交换，从而概括了真正的并发性原则。虽然他们似乎是非常有前途的-因为他们有可能使用的技术，从代数拓扑，以研究并发计算-他们还没有被精确地与以前的模型，本文的目的是填补这一空白。特别是，我们描述了Petri网和立方集之间的附加扩展以前已知的附加Petri网和异步过渡系统之间的尼尔森和Winskel。
英文摘要：
A wide variety of models for concurrent programs has been proposed during the past decades, each one focusing on various aspects of computations: trace equivalence, causality between events, conflicts and schedules due to resource accesses, etc. More recently, models with a geometrical flavor have been introduced, based on the notion of cubical set. These models are very rich and expressive since they can represent commutation between any bunch of events, thus generalizing the principle of true concurrency. While they seem to be very promising - because they make possible the use of techniques from algebraic topology in order to study concurrent computations - they have not yet been precisely related to the previous models, and the purpose of this paper is to fill this gap. In particular, we describe an adjunction between Petri nets and cubical sets which extends the previously known adjunction between Petri nets and asynchronous transition systems by Nielsen and Winskel.
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。
