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The at-most-k constraint is ubiquitous in combinatorial problems, and numerous SAT encodings are available for the constraint. Prior experiments have shown the competitiveness of the sequential-counter encoding for k $>$ 1, and have excluded the parallel-counter encoding, which is more compact that the binary-adder encoding, from consideration due to its incapability of enforcing arc consistency through unit propagation. This paper presents an experiment that shows astounding performance of the binary-adder encoding for the at-most-k constraint.
We present Bicoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the introduction of
In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research community as the
Scaling issues are mundane yet irritating for practitioners of reinforcement learning. Error scales vary across domains, tasks, and stages of learning; sometimes by many orders of magnitude. This can be detrimental to learning speed and stability, cr
Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause length k (k
In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list by reducing the task to an eigenvalue problem in a considerably faster and simpler w