Constraint-based reachability

Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with standard backward or forward exploration strategies. An approach that we call Constraint-based reachability, is proposed to address reachability problems by exploring program states using a constraint model of the whole program. The keypoint of the approach is to interpret imperative constructions such as conditionals, loops, array and memory manipulations with the fundamental notion of constraint over a computational domain. By combining constraint filtering and abstraction techniques, Constraint-based reachability is able to solve reachability problems which are usually outside the scope of backward or forward exploration strategies. This paper proposes an interpretation of classical filtering consistencies used in Constraint Programming as abstract domain computations, and shows how this approach can be used to produce a constraint solver that efficiently generates solutions for reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310

The alldifferent Constraint: A Survey

The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several solving strategies have been designed for this constraint. In this paper we give both a practical overview and an abstract comparison of these different strategies.Comment: 12 pages, 3 figures, paper accepted at the 6th Annual workshop of the ERCIM Working Group on Constraint

A Framework for Decision-based Consistencies

International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones

Intermediary Local Consistencies

International audienceWe propose a new definition for characterizing levels of consistency. A perspective is to provide new tools for classifying filtering algorithms, including incomplete algorithms based on the semantics of constraints

A Class of df-consistencies for Qualitative Constraint Networks

International audienceIn this paper, we introduce a new class of local consis- tencies, called °f-consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition (°) and a mapping f that provides a covering for each relation. We study the connections ex- isting between some properties of mappings f and the relative inference strength of °f-consistencies. The con- sistency obtained by the usual closure under weak com- position is shown to be the weakest element of the class, and new promising perspectives are shown to be opened by °f-consistencies stronger than weak composition. We also propose a generic algorithm that allows us to com- pute the closure of qualitative constraint networks un- der any "well-behaved" consistency of the class. The experimentation that we have conducted on qualitative constraint networks from the Interval Algebra shows the interest of these new local consistencies, in particular for the consistency problem