5.148. imply

Origin

Logic

Constraint

imply​(VAR,​VARIABLES)​

Synonym(s)

rel, ifthen.

Argument(s)

VAR	dvar
VARIABLES	collection​(var−dvar)​

Restriction(s)

VAR≥0

VAR≤1

|VARIABLES|=2

required​(VARIABLES,​var)​

VARIABLES.var≥0

VARIABLES.var≤1

Purpose

Let VARIABLES be a collection of 0-1 variables VAR₁,​VAR₂. Enforce VAR=​(VAR₁⇒VAR₂)​.

Example

​(1,​〈0,​0〉)​

​(1,​〈0,​1〉)​

​(0,​〈1,​0〉)​

​(1,​〈1,​1〉)​

Systems

rel in Gecode, ifthenbool in Jacop, #=> in SICStus.

See also

and, equivalent, nand, nor, or, xor.

Key words

characteristic of a constraint: automaton, automaton without counters.

constraint network structure: Berge-acyclic constraint network.

constraint type: Boolean constraint.

filtering: arc-consistency.

Automaton

Figure 5.148.1 depicts the automaton associated with the imply constraint. To the first argument VAR of the imply constraint corresponds the first signature variable. To each variable VAR_i of the second argument VARIABLES of the imply constraint corresponds the next signature variable. There is no signature constraint.

Figure 5.148.1. Automaton of the imply constraint

Figure 5.148.2. Hypergraph of the reformulation corresponding to the automaton of the imply constraint