Formal Verification of UML2 Timing Diagrams based on Time Petri Nets

2.1. UML2 TD

Timing Diagram (TD) (OMG, 2012) is used to express state change of a value of one or more elements over time. Actually, it is used to further study the model in terms of time and duration constraints and the merge of the different elements such as lifeline, state, message, time constraint and duration constraint (see Figure 1).

Figure 1.

Timing Diagram example [Source: www.sparxsystems.com]

The TD life line shows the change of an item's state over time, while the state represents the set of the attributes values of an object. The duration constraint expresses the maintain time of the object state and the time constraint represents the time where each state transition can be released. Finally, a message represents a communication link between two life lines.

In this work, we propose a formal definition of UML2 TD which is inspired from the work proposed in (Joochim, 2010). So, the TD will be described using a model M_TD as follows:

M_TD = (Lf, Pt, Msg, State, Dc and Tc) where:

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  Lf = {lf₁, .., lf_k} represents a final set of life lines.

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  Pt = {pt₁, .., pt_k} represents a final set of interaction points relying all life lines to asynchronous messages.

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  Msg = {m₁, .., m_k} represents a final set of asynchronous messages exchanged between objects.

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  State = {st₁, .., st_k} represents a final set of objects states.

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  Dc = {dc₁, .., dc_k} represents a final set of duration constraints.

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  Tc = {tc₁, .., tc_k} represents a final set of time constraints.