On the Relative Efficiency of DPLL and OBDDs with Axiom and Join

This paper studies the relative efficiency of ordered binary decision diagrams (OBDDs) and the Davis-Putnam-Logemann-Loveland procedure (DPLL), two of the main approaches to solving Boolean satisfiability instances. Especially, we show that OBDDs, even when constructed using only the rather weak axiom and join rules, can be exponentially more efficient than DPLL or, equivalently, tree-like resolution. Additionally, by strengthening via simple arguments a recent result—stating that such OBDDs do not polynomially simulate unrestricted resolution—we also show that the opposite holds: there are cases in which DPLL is exponentially more efficient out of the two considered systems. Hence DPLL and OBDDs constructed using only the axiom and join rules are polynomially incomparable. This further highlights differences between search-based and compilation-based approaches to Boolean satisfiability.