Three metric domains of processes for bisimulation [chapter]

Franck Breugel
1994 Lecture Notes in Computer Science  
A new metric domain of processes is presented. This domain is located in between two metric process domains introduced by D e B a k k er and Zucker. The new process domain characterizes the collection of image nite processes. This domain has as advantages over the other process domains that no complications arise in the de nitions of operators like sequential composition and parallel composition, and that image nite language constructions like random assignment can be modelled in an elementary
more » ... ay. As in the other domains, bisimilarity and equality coincide in this domain. The three domains are obtained as unique (up to isometry) solutions of equations in a category of 1-bounded complete metric spaces. In the case the action set is nite, the three domains are shown to be equal (up to isometry). For in nite action sets, e.g., equipollent to the set of natural or real numbers, the process domains are proved not to be isometric. Aczel introduces in Acz88] a process domain for non-well-founded sets. For complete metric spaces, process domains are presented by D e B a k k er and Zucker in BZ82, BZ83], and Golson and Rounds in GR83, Gol84]. Aczel shows in Acz88] that processes can be viewed as labelled transition systems. Bisimulation relations on these labelled transition systems induce bisimulation relations on the processes. A process in the de nitions of the operators mentioned above o n P 2 -and P 3 -processes. Unlike the process domain P 2 , the process domain P 3 makes an elementary semantic modelling of image nite language constructions like random assignment possible (cf. Bre94]). (For a detailed overview of metric semantic models the reader is referred to BR92].) Novel in the present paper are the process domain P 3 , w h i c h can be shown to correspond to the class of image nite processes and to be strongly extensional, the detailed comparison of the process domains
doi:10.1007/3-540-58027-1_5 fatcat:6h3hb47cv5gcvahlrq2v5cynk4