Arc consistency and friends

Abstract

A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc consistency, a heavily investigated inference method, and three extensions thereof from the perspective of constraint languages. We conduct a comparison of the studied methods on the basis of which constraint languages they solve, and we present new polynomial-time tractability results for singleton arc consistency, the most powerful method studied.

The collapse of the bounded width hierarchy

“…A different weakening of (2, 3)-minimality is singleton arc consistency (see [12]). An instance is singleton arc consistent if it is 1-minimal and the 1-minimality algorithm succeeds even when we add any constraint of the form "x = a", where x is a variable and a ∈ P x .…”

“…An instance is singleton arc consistent if it is 1-minimal and the 1-minimality algorithm succeeds even when we add any constraint of the form "x = a", where x is a variable and a ∈ P x . The authors in [12] ask whether any singleton arc consistent instance over a bounded width language has a solution. A positive answer would give a more efficient algorithm for solving CSPs over bounded width languages.…”

Decomposing Quantified Conjunctive (or Disjunctive) Formulas

“…∧ α n ), where the x i are variables and where the α i are atomic formulas. These sentences have been approached by researchers possessing a variety of motivations and perspectives [29,32,40,39,34,35,36,9,16,3,4,5,19,18,23,26,25]. In the database literature, they are known as conjunctive queries and are of central interest; the problem of model checking such sentences is also a formulation of the constraint satisfaction problem [40].…”

Tractability in constraint satisfaction problems: a survey

“…Connected row-convex constraints [77] are closed under the ternary median operation which is another example of a majority operation [111]. It has been recently shown that singleton arc-consistency solves CSP( ) when admits a majority polymorphism [40].…”