![](bga.png)
nevertheless the notion of nested CF is briefly men-
tioned, and no explicit formalization for them is pro-
posed.
7 CONCLUSION
In this paper, we first defined an intuitive formaliza-
tion, based on set theory and tree structure, of se-
quence diagrams equipped with combined fragments
that can be nested. The formalization can be adapted
for any kind of semantics. Then, we have extended
the causal semantics by redefining its rules in a syn-
thetic way. The new causal relationship allows to
compute all possible valid traces for SDs with nested
CF that model behaviours of distributed systems, by
avoiding the flattening of SD equipped with (ALT,
OPT, LOOP) CF, hence the compact syntactic repre-
sentation is preserved.
The proposed semantics can serves as basis for
the derivation of traces of UML2.0 SD, as well as
for the definition of an operational semantics that fa-
cilitates the analysis of the SD. Our approach is not
related to any target translation formalism and can
be implemented by any formal method for its veri-
fication, although it is already implemented, (Dhaou
et al., 2015), (Dhaou et al., 2016), by Event-B method
offering powerful tools (Rodin/Pro-B).
Meanwhile, we are extending our proposal to
cover other concepts like the gates and the state in-
variants which allow one to express more complex
behaviours and to cover other CF, in particular those
dedicated to model parallel behaviours and invalid be-
haviours. In addition, we currently study theoretical
properties that are derived from the proposed seman-
tics.
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