Event-Based Semantics of UML 2.X Concurrent Sequence Diagrams for Formal Verification

UML 2.X sequence diagrams (SD) are among privileged scenarios-based approaches dealing with the complexityof modeling the behaviors of some current systems. However, there are several issues related to the standard semantics ofUML 2.X SD proposed by the Object Management Group (OMG). They mainly concern ambiguities of the interpretation ofSDs, and the computation of causal relations between events which is not specifically laid out. Moreover, SD is a semi-formallanguage, and it does not support the verification of the modeled system. This justifies the considerable number of researchstudies intending to define formal semantics of UML SDs. We proposed in our previous work semantics covering the mostpopular combined fragments (CF) of control-flow ALT, OPT, LOOP and SEQ, allowing to model alternative, optional, iterativeand sequential behaviors respectively. The proposed semantics is based on partial order theory relations that permit thecomputation of the precedence relations between the events of an SD with nested CFs. We also addressed the issue ofthe evaluation of the interaction constraint (guard) for guarded CFs, and the related synchronization issue. In this paper,we first extend our semantics, proposed in our previous work; indeed, we propose new rules for the computation of causalrelations for SD with PAR and STRICT CFs (dedicated to modeling concurrent and strict behaviors respectively) as well astheir nesting. Then, we propose a transformational semantics in Event-B. Our modeling approach emphasizes computationof causal relations, guard handling and transformational semantics into Event-B. The transformation of UML 2.X SD into theformal method Event-B allows us to perform several kinds of verification including simulation, trace acceptance, verificationof properties, and verification of refinement relation between SDs.