Constraint Decomposition Based on Tractable Properties

Identifying tractable classes of constraint satisfaction problems (CSPs) has been studied over the past two decades, and is now a very active research domain. Recently, some works have shown the interest of these tractable classes from a different viewpoint. For example, it is known that if there is no broken triangle on each two values of a given variable in an arc-consistent binary CSP, then this variable can be eliminated without changing its satisfiability. Next, it has been proved that even when this rule cannot be applied, it may be the case that for a given pair of values no broken triangle occurs, if this is the case, then we can perform a domain-reduction operation which consists in merging these values while preserving satisfiability. In this paper, we show that partial or total presence of tractable properties in non-binary constraints is sufficient for them to be decomposable into a set of lower arity constraints while preserving equivalence. More precisely, we prove that the presence of bijection or Dual Broken Triangle Property in non-binary constraint permits to decompose it while preserving equivalence.