Constraints and Adaptation Sample Clauses

Constraints and Adaptation. ‌ ( ) Constraint Satisfaction Problems A connection graph [28] is a tuple N, A, a, c , where N is a set A a ∈ A c a tuple of nodes connected by h, xi xj when i ƒ= j. Additionally, A = ∪kAk is a ranked set: of nodes, is a set of arcs, is an interface arc, and is a connection function. Connection function c = Sk(Ak → Nk) is a correspondence between arcs and nodes: c(h) = (x1, . . . , xk) is S → ← | ←

Constraints and Adaptation. Constraint Satisfaction Problems A connection graph [28] is a tuple N, A, a, c , where N is a set A a ∈ A c a tuple of nodes connected by h, xi xj when i /= j. Additionally, A = ∪kAk is a ranked set: of nodes, is a set of arcs, is an interface arc, and is a connection function. Connection function c = Sk(Ak → Nk) is a correspondence between arcs and nodes: c(h) = ⟨x1, . . . , xk⟩ is S → ← | ← ⟨ ⟩ ∈ ← {⟨ ⟩| ∀ ∈ ⟨ ⟩| ∈ } each h Ak is an arc connected to k nodes. We refer to the connection graph by writing: a G, where G = N, A, c . Labeled arcs are sometimes used to introduce additional functions in the tuple assigning a label to every arc. A network of constraints [28] is a pair C = a G l, where a G is a finite connection graph, whose nodes are variables and arcs are constraints; l is a labelling function l : k(Ak P (Uk)), where U is a finite set of values for the variables of C; P (Uk) is the set of all k-relations on U . Solving a network of constraints is called a constraint satisfaction problem (CSP). Let C = a ← G | l, G = ⟨N, A, a, c⟩, n = #N , and ⟨x1, . . . , xn⟩ be any ordering of the variables of N . Given that v = ⟨v1, . . . , vn⟩ is n-tuple of values of U , let us set v|⟨xi1,...,xim⟩ = ⟨vi1, . . . , vim⟩. The solution of network C is the set v1, . . . , vn c(a) : b A, v1, . . . , vn c(b) l(b) . In other words, the CSP for a network of constraints is to find the set of all the assignments of the variables connected by the interface arc such that every such assignment can be extended to an assignment of all the variables in N which satisfies all the constraints in A [28]. ← |