This paper describes a computer-assisted non-existence proof of 9-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29-comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. This closes the two smallest open… (More)
This paper presents the pl-nauty library, a Prolog interface to the nauty graph-automorphism tool. Adding the capabilities of nauty to Prolog combines the strength of the " generate and prune " approach that is commonly used in logic programming and constraint solving, with the ability to reduce symmetries while reasoning over graph objects. Moreover, it… (More)
We apply the pigeonhole principle to show that there must exist Boolean functions on 7 inputs with a multiplicative complexity of at least 7, i.e., that cannot be computed with only 6 multiplications in the Galois field with two elements.
This paper introduces a general methodology that applies to solve graph edge-coloring problems and demonstrates its use to compute the Ramsey number R(4, 3, 3). The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found " soon ". Yet, its precise value has remained unknown for more than 50 years. The proposed… (More)