D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange

16 F. Massacci and L.M.S. Tran
Round rectangles represent goal nodes, circles are compound nodes, and diamonds denotes
observable nodes. Goals with a same number refer to the same objective.
Fig. 6 The hypergraph of the case study described in §2 with evolution rules embedded.
• For each decomposition 〈g, S g〉, create a compound node c. Then create a dotted
edge 〈c, g, 1〉 connecting c to g. For each goal g ′ ∈ S g, create a full edge 〈g ′ , c, 1〉
connecting g’ to c.
• For each observable rule [ j ff
SM α pα i
−−→ SMi
α , create an observable node o.
Then create full edges ˙o, g α, p α ¸
i where gα denotes the top goal of SM α .
This hypergraph has three kinds of nodes: goal node, observable node, and
compound node. These kinds of nodes orderly correspond to goals, observable
rules, and decomposition of goals. Besides, there are two kinds of edges: full edges
and dotted edges. The full edge connects an observable node or compound node to
another observable or goal node. The full edge connecting an observable node to
a goal node denotes a potential evolution possibility of the goal node. Therefore,
goal nodes connected to an observable node always have the same name, determining
several potential evolution possibilities of the observable rule corresponding to
this observable node. Meanwhile, full edges connecting a compound node to other
nodes together with a dotted edge connecting this compound node to another goal
node represent a decomposition.
Example 4 (Hypergraph) To the illustrative purpose, Fig. 6 describes the hypergraph
of the case study with two observable rules r o1 and r o2 for goal g 2 −Optimal
arrival sequence applied and goal g 5 −Data exchanged, respectively. Notice that, goals with
a same number refer to the same objective, and only one of them is fully labeled
to save the space.
In this figure, white goals indicate objectives identified at current time. Meanwhile,
gray goals denote objectives introduced if evolution happens. In rule r o1 ,
discussed in Example 2, the original subpart {g 5 ← g 9 } might evolve to either