摘要
Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs’ notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations.
摘要译文
我们的具体目标是在基于多集合双模拟的共同组织框架中呈现普通的双模拟和概率双模拟。为此，我们展示了如何通过充分的自然变换将潜在的权力和概率分布函子与多重函数函数相关联。这导致我们在本文中调查的一般主题：从函子F到另一个G的自然转换将F-双模拟变换成G-双模拟，但是，一般来说，不可能在F-双模拟方面表达G-双模拟。然而，它们的特征可以是考虑休斯和雅各布的模拟概念，作为函子F的顺序，F与G相关的自然变换的epi-mono分解引起的等价性。我们还考虑了交替概率系统的情况，其中非确定性和概率选择是混合的，尽管只是部分地，并将所有这些结果扩展到分类模拟。
David de Frutos Escrig1;Miguel Palomino1;Ignacio Fábregas1. Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations. Formal Techniques for Networked and Distributed Systems – FORTE 2008[M].DE: Springer;LNCS, 2008: 283-298