On the upper bounds of (1,0)-super solutions for the regular balanced random (k,2s)-SAT problem

Abstract

This paper explores the conditions which make a regular balanced random (k,2s)-CNF formula (1,0)-unsatisfiable with high probability. The conditions also make a random instance of the regular balanced (k − 1,2(k − 1)s)-SAT problem unsatisfiable with high probability, where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random (k − 1,2(k − 1)s)-CNF formula. Let F be a regular balanced random (k,2s)-CNF formula where k ⩾ 3, then there exists a number s₀ such that F is (1,0)-unsatisfiable with high probability if s > s₀. A numerical solution of the number s₀ when k ∈ {5, 6,…, 14} is given to conduct simulated experiments. The simulated experiments verify the theoretical result. Besides, the experiments also suggest that F is (1,0)-satisfiable with high probability if s is less than a certain value.