Section: New Results

Constraint and Abstract Interpretation

Participants : Marie Pelleau, Charlotte Truchet, Fredéric Benhamou, Antoine Miné.

We apply techniques from Abstract Interpretation (AI), a general theory of semantic abstractions, to Constraint Programming (CP), which aims at solving hard combinatorial problems with a generic framework based on first-order logics. We highlight some links and differences between these fields: both compute fix-points by iteration but employ different extrapolation and refinement strategies; moreover, consistencies in Constraint Programming can be mapped to non-relational abstract domains.

• In a first step, we redefine all the components of CP on abstract domains, instead of the usual cartesian, domain-specific domains (boxes or integer sets), obtaining a generic method that can be specified for any of the AI abstract domains.

• In a second step, we then use the correspondences between AI and CP to build an abstract constraint solver that leverages abstract interpretation techniques (such as relational domains) to go beyond classic solvers. We present encouraging experimental results obtained with our prototype implementation, called AbSolute. In particular, AbSolute is able to solve problems on both discrete and continuous variables.

The work is done in collaboration with Antoine Miné .

A corresponding paper A constraint solver based on abstract domains [26] will appear at the 14th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI'13) .