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Modular Constraint Solver Cooperation via Abstract Interpretation

Published online by Cambridge University Press:  22 September 2020

PIERRE TALBOT Open the ORCID record for PIERRE TALBOT [Opens in a new window] ,
ÉRIC MONFROY  and
CHARLOTTE TRUCHET
PIERRE TALBOT
Affiliation:
Interdisciplinary Centre for Security, Reliability and Trust (SNT), University of Luxembourg, Esch-sur-Alzette, Luxembourg (e-mail: pierre.talbot@uni.lu)
ÉRIC MONFROY
Affiliation:
University of Angers, Angers, France (e-mail: eric.monfroy@univ-angers.fr)
CHARLOTTE TRUCHET
Affiliation:
University of Nantes, Nantes, France (e-mail: charlotte.truchet@univ-nantes.fr)
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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.

Keywords

abstract domainssolver cooperationmodularityconstraint programming
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 848 - 863
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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