# dwavebinarycsp.irreducible_components¶

irreducible_components(constraint)[source]

Determine the sets of variables that are irreducible.

Let V(C) denote the variables of constraint C. For a configuration x, let x|A denote the restriction of the configuration to the variables of A. Constraint C is reducible if there is a partition of V(C) into nonempty subsets A and B, and two constraints C_A and C_B, with V(C_A) = A and C_B V(C_B) = B, such that a configuration x is feasible in C if and only if x|A is feasible in C_A and x|B is feasible in C_B. A constraint is irreducible if it is not reducible.

Parameters

constraint (`Constraint`) – Constraint to attempt to reduce.

Returns

List of tuples in which each tuple is a set of variables that is irreducible.

Return type

Examples

This example reduces a constraint, created by specifying its valid configurations, to two constraints. The original constraint, that valid configurations for a,b,c are 0,0,1 and 1,1,1, can be represented by two reduced constraints, for example, (c=1) & (a=b). For comparison, an attempt to reduce a constraint representing an AND gate fails to find a valid reduction.

```>>> const = dwavebinarycsp.Constraint.from_configurations([(0, 0, 1), (1, 1, 1)],
...                                                       ['a', 'b', 'c'], dwavebinarycsp.BINARY)
>>> dwavebinarycsp.irreducible_components(const)
[('c',), ('a', 'b')]
>>> const_and = dwavebinarycsp.Constraint.from_configurations([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 1)],
...                                                           ['a', 'b', 'c'], dwavebinarycsp.BINARY)
>>> dwavebinarycsp.irreducible_components(const_and)
[('a', 'b', 'c')]
```