D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange
D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange
D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange
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14 F. Massacci and L.M.S. Tran<br />
DMAN1<br />
DMAN<br />
ATM<br />
SYSTEM<br />
AMAN<br />
AMAN1<br />
ATM<br />
SYSTEM<br />
AMAN<br />
AMAN1<br />
AMAN11<br />
DMAN2<br />
AMAN2<br />
AMAN2<br />
AMAN12<br />
(a) Multi-part evolution scenario<br />
(b) Multi-step evolution scenario<br />
The left (a) exemplifies a multi-part evolution, where a big ATM system has two separated subsystems (parts),<br />
AMAN and DMAN, which may evolve independently. Meanwhile, the right (b) illustrates a multi-step scenario.<br />
After AMAN evolves to AMAN 1, it continues to evolve to either AMAN 11 or AMAN 12.<br />
Fig. 5 Complex evolution scenarios.<br />
7 More Complex Evolution Scenarios<br />
In practice, evolutions can fall into one of two scenarios: multi-part and multi-step<br />
(or combination of these scenarios).<br />
The multi-part scenario indicates evolutions in different parts of a big enterprise<br />
model, as illustrated in Fig. 5(a). This is a case that a system comprises of several<br />
subsystems which are relatively independent. For instance, in the whole ATM<br />
system, the AMAN subsystem (Arrival Management System) is more or less independent<br />
with the DMAN (Departure Management System) subsystem even though<br />
they can exchange data. Thus AMAN can evolves independently with DMAN. We<br />
call evolution in subparts of the model as local evolution.<br />
The multi-step evolution scenario determines the case that the system is iteratively<br />
evolving. In Fig. 5(b), the AMAN subsystem of ATM, after evolving to<br />
AMAN 1 , may continue to evolve to either AMAN 11 or AMAN 12 . Suppose that the<br />
evolution of AMAN to AMAN 1 or AMAN 2 is subject to an observable rule r o1 ;<br />
and the evolution of AMAN 1 to AMAN 11 or AMAN 12 is subject to an observable<br />
rule r o2 . The global evolution of AMAN, in this case, is a 2-step evolution. Obviously,<br />
r o2 can only be effective only if r o1 happens in the first step/phase, AMAN<br />
−→ AMAN 1 . We call the relationship between r o1 and r o2 evolution-dependent<br />
relationship, which are formally defined as follows.<br />
Definition 5 (Evolution-dependent relation) Given two observable rules r o1 =<br />
S n EM p o<br />
i<br />
−→ EM i and ro2 = S j ff<br />
EM ′ p j<br />
−→ EM j<br />
′ , the rule r o2 is evolution-dependent<br />
i<br />
to the rule r o1 , denoted as r o1 r o2 if there exists a possibility EM p i<br />
−→ EM i of r o1<br />
such that EM’ is a subset (or equal) of EM i .<br />
r o1<br />
i<br />
r o2 ⇔ ∃EM p i<br />
−→ EM i ∈ r o1 .EM ′ ⊆ EM i (2)<br />
To this end we define the evolutionary enterprise model that take into account<br />
all complex evolution scenarios as follows.<br />
Definition 6 (Evolutionary enterprise model) An evolutionary enterprise model<br />
eEM is a quadruplet 〈EM, R o, R c, Dep〉 where: