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We show that tree-like OBDD proofs of unsatisfiability require an exponential increase (s rarr 2s Omega(1)) in proof size to simulate unrestricted resolution, and that unrestricted OBDD proofs of unsatisfiability require an almost-exponential increase (s rarr 22(log s) Omega(1)) in proof size to simulate Res (O(log n)). The "OBDD proof system" that we consider has lines that are ordered binary decision diagrams in the same variables as the input formula, and is allowed to combine two previously derived OBDDs by any sound inference rule. In particular, this system abstracts satisfiability algorithms based upon explicit construction of OBDDs and satisfiability algorithms based upon symbolic quantifier elimination.
Date of Conference: 23-26 June 2008