D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange

sectors. And there is 42% of probability that goal G 5 is refined to either goals {G 9 , G 12 },
or goals {G 9 , G 13 }. Finally, there is 46% of probability that goal G 5 is refined to goals
{G 9 , G 12 , G 13 }.
{G 9 , G 12 }, {G 9 , G 13 } and {G 9 , G 12 , G 13 } are called design alternatives for goal G 5 .
Figure 11. The goal model of Figure 5 with potential evolutions. Shaded goals denote potential
changes in future, and the diamond nodes denote different possibilities that a goal may change.
In order to compute the maximal belief and the residual risk, we transform the
hypergraph in Figure 10 into the hypegraph that includes goals and the possible
evolution rules illustrated in Figure 11. The hypergraph includes two evolution rules for
goal G 2 - Optimal arrival sequence applied and goal G 5 –Data Exchanged. Notice that,
goals with a same number refer to the same objective, and only one of them is fully
labeled to save the space. White goals indicate goals existing before evolution, while
gray goals denote goals introduced when evolution happens. As already described G 5
might evolve to either {G 9 , G 12 , G 13 } and {G 9 , G 12 } or {G 9 , G 13 } with a probability of
46% and 42%, respectively. The original part might stay unchanged with a probability
of 12%. Similarly, goal G 2 also evolves to two other possibilities with probabilities of
45% and 40%. It stays the same with a probability of the 15%.
Each node in the hypergraph is associated with a data structure called design
alternative table (DAT). The DAT is a set of tuples ⟨S, mb, rr, T i ⟩ where S is a set of leaf
goals necessary to fulfill this node; mb, rr are the maximum belief and residual risk of
this node, respectively; T i is a possible design alternative in the observable evolution
rule associated with the node. Obviously, two tuples in a DAT which have a same T i are
two design alternatives of an observable evolution possibility. For a leaf node L, the
DAT of L has only one row which is ⟨{L}, 1, 0, ∅⟩. The DATs of leaf nodes are then
propagated upward to predecessor nodes (ancestors). This propagation is done by two
operators join (⊗) and concat (⊕). Also via these operators, DAT of a predecessor
node is generated using their successor's DATs. join (⊗) and concat (⊕) are defined
as follows.
D.3.3 Algorithms for Incremental Requirements Models
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