Observational Refinement and Merge for Disjunctive MTSs.

Modal Transition System (MTS) is a well studied formalism for partial model specification. It allows a modeller to distinguish between required, prohibited and possible transitions. Disjunctive MTS (DMTS) is an extension of MTS that has been getting attention in recent years. A key concept for (D) MTS is refinement, supporting a development process where abstract specifications are gradually refined into more concrete ones. Refinement comes in different flavours: strong, observational (where Gamma-labelled transitions are taken into account), and alphabet (allowing the comparison of models defined on different alphabets). Another important operation on (D) MTS is that of merge: given two models M and N, their merge is a model P which refines both M and N, and which is the least refined one. In this paper, we fill several missing parts in the theory of DMTS refinement and merge. First and foremost, we define observational refinement for DMTS. While an elementary concept, such a definition is missing from the literature to the best of our knowledge. We prove that our definition is sound and that it complies with all relevant definitions from the literature. Based on the new observational refinement for DMTS, we examine the question of DMTS merge, which was defined so far for strong refinement only. We show that observational merge can be achieved as a natural extension of the existing algorithm for strong merge of DMTS. For alphabet merge however, the situation is different. we prove that DMTSs do not have a merge under alphabet refinement.