Modular Constraint Solver Cooperation via Abstract Interpretation
This work addresses the problem of integrating diverse constraint solvers for researchers and practitioners in constraint programming, offering a more flexible alternative to fixed schemes like SMT, though it is incremental in building on existing abstract interpretation theory.
The paper tackles the difficulty of cooperation among constraint solvers with different theoretical foundations by proposing a modular framework based on abstract interpretation, where cooperation schemes are viewed as abstract domain combinations, and it contributes two new schemes: interval propagators completion and delayed product, with full implementation demonstrated on the flexible job shop scheduling problem.
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.