Proving unsatisfiability for problems with constant cubic sparsity

This paper presents a perspective on a previously studied heuristic tree search algorithm for the NP-complete “3SAT” satisfiability problem, which synthesizes results by Brown, Franco, Purdom, and others. It is shown that when an a priori calculation indicates a random, nontrivial 3SAT formula is very likely unsatisfiable, then the heuristic algorithm is expected to prove unsatisfiability in a search tree with size essentially independent of the problem size, and bounded by a constant that depends only on the ratio of the number of clauses to the cube of the number of variables.