In eXplainable Constraint Solving (XCS), it is common to extract a Minimal Unsatisfiable Subset (MUS) from a set of unsatisfiable constraints. This helps explain to a user why a constraint specification does not admit a solution. Finding MUSes can be computationally expensive for highly symmetric problems, as many combinations of constraints need to be considered. In the traditional context of solving satisfaction problems, symmetry has been well studied, and effective ways to detect and exploit symmetries during the search exist. However, in the setting of finding MUSes of unsatisfiable constraint programs, symmetries are understudied. In this paper, we take inspiration from existing symmetry-handling techniques and adapt well-known MUS-computation methods to exploit symmetries in the specification, speeding-up overall computation time. Our results display a significant reduction of runtime for our adapted algorithms compared to the baseline on symmetric problems.

Constraint programming (CP) modeling languages, like MiniZinc, Essence and CPMpy, play a crucial role in making CP technology accessible to non-experts. Both solver-independent modeling frameworks and solvers themselves are complex pieces of software that can contain bugs, which undermines their usefulness. Mutational fuzz testing is a way to test complex systems by stochastically mutating input and verifying preserved properties of the mutated output. We investigate different mutations and verification methods that can be used on the constraint specifications directly. This includes methods proposed in the context of SMT problem specifications, as well as new methods related to global constraints, optimization, and solution counting/preservation. Our results show that such a fuzz testing approach improves the overall code coverage of a modeling system compared to only unit testing, and is able to find bugs in the whole toolchain, from the modeling language transformations themselves to the underlying solvers.

Decision trees are among the most popular classification models in machine learning. Traditionally, they are learned using greedy algorithms. However, such algorithms have their disadvantages: it is difficult to limit the size of the decision trees while maintaining a good classification accuracy, and it is hard to impose additional constraints on the models that are learned. For these reasons, there has been a recent interest in exact and flexible algorithms for learning decision trees. In this paper, we introduce a new approach to learn decision trees using constraint programming. Compared to earlier approaches, we show that our approach obtains better performance, while still being sufficiently flexible to allow for the inclusion of constraints. Our approach builds on three key building blocks: (1) the use of AND/OR search, (2) the use of caching, (3) the use of the CoverSize global constraint proposed recently for the problem of itemset mining. This allows our constraint programming approach to deal in a much more efficient way with the decompositions in the learning problem.

Multi-Valued Decision Diagrams (MDDs) are instrumental in modeling combinatorial problems with Constraint Programming.In this paper, we propose a related data structure called sMDD (semi-MDD) where the central layer of the diagrams is non-deterministic.We show that it is easy and efficient to transform any table (set of tuples) into an sMDD.We also introduce a new filtering algorithm, called Compact-MDD, which is based on bitwise operations, and can be applied to both MDDs and sMDDs.Our experimental results show the practical interest of our approach, both in terms of compression and filtering speed.

Table constraints are very useful for modeling combinatorial constrained problems, and thus play an important role in Constraint Programming (CP). During the last decade, many algorithms have been proposed for enforcing the property known as Generalized Arc Consistency (GAC) on such constraints. A state-of-the art GAC algorithm called Compact-Table (CT), which has been recently proposed, significantly outperforms all previously proposed algorithms. In this paper, we extend this algorithm in order to deal with both short supports and negative tables, i.e., tables that contain universal values and conflicts. Our experimental results show the interest of using this fast general algorithm.