3 papers
cs.DM2016
Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-Conquer
Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek
The boolean Pythagorean Triples problem has been a longstanding open problem in Ramsey Theory: Can the set N = of natural numbers be divided into two parts, such th…
cs.DM2016
Unsatisfiable hitting clause-sets with three more clauses than variables
Oliver Kullmann, Xishun Zhao
The topic of this paper is the Finiteness Conjecture for minimally unsatisfiable clause-sets (MUs), stating that for each fixed deficiency (number of clauses minus number of variab…
cs.DM2015
Parameters for minimal unsatisfiability: Smarandache primitive numbers and full clauses
Oliver Kullmann, Xishun Zhao
We establish a new bridge between propositional logic and elementary number theory. The main objects are "minimally unsatisfiable clause-sets", short "MUs", unsatisfiable conjuncti…