Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

CSP deals with two classical problems: i) solution problem and ii) satisfaction
problem. The solution problem is concerned with finding the solutions
satisfying all the constraints. The satisfaction problem requires clarification
about the existence of a solution. An algorithm that is capable of determining
the satisfaction of a constraint is called a ‘Constraint Solver’. Since, a
satisfaction problem also constructs a solution as a bi-product, we emphasize
the satisfaction problem over the solution problem.
Definition 19.8: A linear Constraint is a conjunction of linear equation /
inequalities.
For example, {(x+ y ≤ 2) Λ (x ≤ 1) Λ (y ≤ 1)} is a linear constraint as it is a
conjunction of linear inequalities.
Definition 19.9: A Constraint is called a Boolean constraint, if it comprises
of Boolean variables, having only two values: true and false.
Boolean constraints include operators like AND (&), OR (∨), implication
(→), bi-directional implication (↔) and exclusive–OR (⊕) . It is to be noted
that we deliberately used & for AND instead of ‘Λ’ as it is used for
conjunction of constraints in an expression.
Definition 19.10: A variable x is determined by a set of constraints C, if
every solution of C is a solution of x= e, where e is a variable-free
expression. We illustrate it in the next section.
19.3 Constraint Propagation in Networks
Determination of the value of variables and their substitution in other
constraints simplify them, which subsequently lead to the solution of the CSP.
For example, let us consider a simple circuit comprising of two resistances
and a D.C. cell (fig.19.1).
+
-
V
I
I1
V1
R1
Fig.19.1: A simple circuit.
V2
R2
I2