Branching Time Semantics for UML 2.0 Sequence Diagrams

Abstract

This paper presents formal definitions for UML Sequences Diagrams based on branching time semantics and partial orders in a denotational style. The obtained graphs are close to lattices and specify faithfully the intended behaviors rather than trace based semantics. We also define few generalized algebraic operations on graphs so that it makes it easy to provide formal definitions in a compositional manner to interaction operators. Next we extend our formalism with logical clocks and time formulas over values of these clocks to express timing constraints of complex systems. We present also some algorithms to extract time annotations that adorn sequence diagrams and transform them into timing constraints in our timed graphs. Obviously, this approach alleviates more the hard task of consistency checking between UML diagrams, specifically interaction diagrams with regards to state diagrams. Timeliness and performance analysis of timed graphs related to sequence diagrams could take advantages of works on model checking of timed automata.

The many meanings of UML 2 Sequence Diagrams: a survey

“…The author of [17] presents a denotational semantics based on partial orders. It assigns to each fragment a graph containing the OccurrenceSpecifications and their relations.…”

Formal Verification of UML MARTE Specifications Based on a True Concurrency Real Time Model

“…Sequence diagrams are semi-formal notation, in other words the syntax and semantics notations are open to different interpretations. In the literature, there are several research papers that address the formal formalization of sequence diagrams [32,33,34,35,36,37,38,39,40,41]. Among these works, the approach of [41] is an interesting one as a formal translation.…”

A Logic-Based Approach for the Verification of UML Timed Models

“…Compared to the previous ones, they provide a detailed analysis of the neg operator. The work presented by Hammal [Hammal 2006] proposes a semantics based on a branching time structure for Sequence Diagrams. The branching time structure is represented by means of graphs annotated with time information.…”

“…He suggests that the timed Petri net that corresponds to the State Machine Diagram can then be checked against the constraints imposed by a Sequence Diagram. It would be interesting to understand how this could be done by exploiting the semantics for Sequence Diagrams proposed by the same author [Hammal 2006], but unfortunately no further details are provided. Choppy et al [Choppy et al 2011] propose a translation of UML state diagrams into Colored Petri nets, and the verification of desired properties can be carried out automatically.…”