On the OBDD-Representation of General Boolean Functions
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Resolution and binary decision diagrams cannot simulate each other polynomially
Discrete Applied Mathematics - The renesse issue on satisfiability
Extended resolution simulates binary decision diagrams
Discrete Applied Mathematics
On the Relative Efficiency of Resolution-Like Proofs and Ordered Binary Decision Diagram Proofs
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
A direct construction of polynomial-size OBDD proof of pigeon hole problem
Information Processing Letters
On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
Extended resolution proofs for conjoining BDDs
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
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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.