Open Maps (at) Work
Open Maps (at) Work
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在工作中打开地图
DOI：
10.7146/brics.v2i23.19925
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发表时间：
1995
影响因子：
4.4
通讯作者：
M. Nielsen
中科院分区：
文献类型：
--
作者：
A. Cheng;M. Nielsen
帕克和米尔纳（Park and Milner）定义的三症的概念已成为过程代数领域的运营等效性最基本的信息之一。属性，它还证明了自己适用于众多平行计算模型，以及诸如Petri Nets和功能语言的语义。在该领域，Joyal，Nielsen和Winskel的大量研究之间的差异最近提出了一个抽象类别的分型，他们确定了满足某些“路径提升”特性的形态的跨度，这可能是一个可能的抽象定义他们在[JNW93]中表明，他们可以捕获公园和米尔纳的仿真。通过显示众所周知的两次仿真和等价的代表性选择，例如Hennessy的测试等价，Milner和Sangiorgi的Barbed Bisimulution以及Larsen和Skou的概率分配，在开放的地图和之后捕获了Skou的概率，因此适用于“实践”。 ，拟议的开放地图概念似乎是成功的。
The notion of bisimilarity, as defined by Park and Milner, has turned out to be one of the most fundamental notions of operational equivalences in the field of process algebras. Not only does it induce a congruence (largest bisimulation) in CCS which have nice equational properties, it has also proven itself applicable for numerous models of parallel computation and settings such as Petri Nets and semantics of functional languages. In an attempt to understand the relationships and differences between the extensive amount of research within the field, Joyal, Nielsen, and Winskel recently presented an abstract categorytheoretic definition of bisimulation. They identify spans of morphisms satisfying certain “path lifting” properties, so-called open maps, as a possible abstract definition of bisimilarity. In [JNW93] they show, that they can capture Park and Milner’s bisimulation. The aim of this paper is to show that the abstract definition of bisimilarity is applicable “in practice” by showing how a representative selection of well-known bisimulations and equivalences, such as e.g. Hennessy’s testing equivalence, Milner and Sangiorgi’s barbed bisimulation, and Larsen and Skou’s probabilistic bisimulation, are captured in the setting of open maps and hence, that the proposed notion of open maps seems successful. Hence, we confirm that the treatment of strong bisimulation in [JNW93] is not a one-off application of open maps.