Bisimulation for probabilistic transition systems: a coalgebraic approach
Bisimulation for probabilistic transition systems: a coalgebraic approach
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DOI：
10.1016/s0304-3975(99)00035-3
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发表时间：
1999-06-28
影响因子：
1.1
通讯作者：
Rutten, JJMM
中科院分区：
文献类型：
--
作者：
de Vink, EP;Rutten, JJMM
由Larsen和Skou提出的离散概率转移系统的互模拟概念与Aczel和Mendler在集合函子意义上的共代数定义相一致，该定义将简单概率分布的集合与一个集合相关联。这种共代数公式使得将离散概率转移系统和概率双模拟的概念推广到包含Borel概率测度的连续集合成为可能。一个函子M-1的介绍，产量的度量空间的Borel概率措施的集合。在合理的条件下，这个函子准确地捕获广义概率双相似性。最后的余代数范式的函子的基础上M-1的应用，然后产生一个内部完全抽象的语义域的概率互模拟，因此非常适合于解释概率规范和随机规划的概念。(C)1999 Elsevier Science B. V.保留所有权利。
The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor, which associates to a set its collection of simple probability distributions. This coalgebraic formulation makes it possible to generalize the concepts of discrete probabilistic transition system and probabilistic bismulation to a continuous Setting involving Borel probability measures. A functor M-1 is introduced that yields for a metric space its collection of Borel probability measures. Under reasonable conditions, this functor exactly captures generalized probabilistic bisimilarity. Application of the final coalgebra paradigm to a functor based on M-1 then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation, which is therefore well suited for the interpretation of probabilistic specification and stochastic programming concepts. (C) 1999 Elsevier Science B.V. All rights reserved.