The Representational Power of Conjunctive Normal Form

There is continuing research interest in comparison of the complexity of problems within the class NP-Complete. This paper examines the representational power of conjunctive normal form Boolean expressions to establish a proper hierarchy for finite languages, where the language of an expression is defined to be the set of bit strings corresponding to its satisfying assignments. The increasing representational complexity parallels and perhaps explains the increasing complexity of k-SAT algorithms for higher values of k. The hierarchy provides a general framework for comparisons of satisfiability algorithms and leads to the conclusion that logical resolution is not a good algorithm for satisfiabiltiy testing.