A Boolean formula in a conjunctive normal form is called a (k, s) - formula if every clause contains exactly k variables and every variable occurs in at most s clauses. The (k,s) -- SAT problem is the SATISFIABILITY problem restricted to (k,s) -- formulas. It is proved that for every k ≥ 3 there is an integer f(k) such that (k, s) -- SAT is trivial for s ≤ f(k) (because every (k, s) -- formula is satisfiable) and is NP-complete for s ≥ f(k) + 1. Moreover, f(k) grows exponentially with k, namely, [2k/ck] ≤ f(k) ≤ 2k-1 - 2k-4 - 1 for k ≥ 4.
ASJC Scopus subject areas
- Computer Science(all)