In this paper we show how the testing equivalences and preorders on transition systems may be interpreted as instances of generalized bisimulation equivalences and prebisimulation preorders. The characterization relies on defining transformations on the transition systems in such a way that the testing relations on the original systems correspond to (pre)bisimulation relations on the altered systems. Using these results, it is possible to use algorithms for determining the (pre)bisimulation relations in the case of finite-state transition systems to compute the testing relations.

This paper describes a method for merging behavior specifications modeled by transition systems. Given two behavior specifications B1 and B2, Merge(B1, B2) defines a new behavior specification that extends B1 and B2. Moreover, provided that a necessary and sufficient condition holds, Merge(B1, B2) is a cyclic extension of B1 and B2. In other words, Merge(B1, B2) extends B1 and B2, and any cyclic trace in B1 or B2 remains a cyclic in Merge(B1, B2). Therefore, in the case of cyclic traces of B1 or B2, Merge(B1, B2) transforms into Merge(B1, B2), and may exhibit, in a recursive manner, behaviors of B1 and B2. If Merge(B1, B2) is a cyclic extension of B1 and B2, then Merge(B1, B2) represents the least common cyclic extension of B1 and B2. This approach is useful for the extension and integration of system specifications. 1 Introduction Formal specifications play an important role in the development life cycle of systems. They capture the user requirements. They can be validated against suc...

Labeled transition systems (lts) provide an operational semantics for many specification languages. In order to abstract unrelevant details of lts's, many behavioural equivalences have been defined; here observation equivalence is considered. We are interested in the following problem: Given a finite lts, which is the minimal observation equivalent lts corresponding to it ? It is well known that the number of states of an lts can be minimized by applying an relational coarsest partition algorithm. However, the obtained lts is not unique (up to the renaming of the states): for an lts there may exist several observation equivalent lts's which have the minimal number of states but varying number of transitions. In this paper we show how the number of transitions can be minimized, obtaining a unique lts. CR categories: F.1.1, F.3.1. Key words: Labeled transition system, Observation equivalence, Minimization, Uniqueness. 1 Introduction. In order to discern the relevant properties of a ...