Modular Constraint Solver Cooperation via Abstract Interpretation

TL;DR

This paper introduces a modular framework for cooperation among constraint solvers using abstract interpretation, enabling flexible combination of solvers and schemes for improved problem solving.

Contribution

It presents a novel modular approach to solver cooperation via abstract domain combinations, including new schemes like interval propagators and delayed product.

Findings

Framework allows seamless addition of solvers and schemes.

Implemented approach demonstrates effectiveness on scheduling problems.

New schemes improve constraint exchange and control in cooperation.

Abstract

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem. Under consideration for acceptance in TPLP.