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Bisimulation as a Logical Relation
arXiv - CS - Logic in Computer Science Pub Date : 2020-03-30 , DOI: arxiv-2003.13542
Claudio Hermida and Uday Reddy and Edmund Robinson and Alessio Santamaria

We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system, and the general result is that a relation $R$ between two transition systems on state spaces $S$ and $T$ is a bisimulation if and only if the derived algebraic structures are in the logical relation automatically generated from $R$. We show that this approach works for the original Park-Milner bisimulation and that it extends to weak bisimulation, and branching and semi-branching bisimulation. The paper concludes with a discussion of probabilistic bisimulation, where the situation is slightly more complex, partly owing to the need to encompass bisimulations that are not just relations.

中文翻译:

作为逻辑关系的互模拟

我们研究了如何使用逻辑关系技术来表征各种形式的互模拟。所采取的方法是每种形式的互模拟对应于一个从转移系统导出的代数结构,一般结果是状态空间 $S$ 和 $T$ 上的两个转移系统之间的关系 $R$ 是互模拟如果和仅当导出的代数结构处于从 $R$ 自动生成的逻辑关系中时。我们表明这种方法适用于原始的 Park-Milner 互模拟,并且它扩展到弱互模拟,以及分支和半分支互模拟。本文最后讨论了概率互模拟,其中的情况稍微复杂一些,部分原因是需要包含不仅仅是关系的互模拟。
更新日期:2020-03-31
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