作为普通互模拟与概率互模拟通用框架的多重集互模拟
Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations
AI总结：
该研究基于多重集互模拟构建共代数通用框架，通过自然变换关联幂集、概率分布函子与多重集函子，结合满单分解诱导的等价与模拟概念刻画互模拟关系，还部分研究交替概率系统并推广至范畴模拟。
摘要：
我们的具体目标是，在基于多重集互模拟的通用共代数框架下呈现普通互模拟与概率互模拟。为此，我们展示了如何通过恰当的自然变换，将底层的幂集函子与概率分布函子和多重集函子关联起来。这引出了本文研究的一般性主题：从函子F到函子G的自然变换可将F-互模拟转化为G-互模拟，但通常无法用F-互模拟来表述G-互模拟。不过，通过引入Hughes与Jacobs提出的模拟概念，将F与G之间自然变换的满单分解所诱导的等价关系作为函子F上的序关系，就可以刻画G-互模拟。我们还部分探讨了非确定性选择与概率选择混合的交替概率系统的情形，并将所有这些结果推广到范畴模拟。
英文摘要：
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.
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