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An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams. (English) Zbl 1141.03028
The main result of the paper is an exponential lower bound on the size of proofs in a propositional proof system operating with ordered binary decision diagrams (OBDD), introduced by A. Atserias, P. Kolaitis and M. Vardi [“Constraint propagation as proof system”, Lect. Notes Comput. Sci. 3258, 77–91 (2004)]. A variant of feasible interpolation holds for OBDD refutations as a corollary to the author’s feasible interpolation theorem for semantic derivations [J. Symb. Log. 62, No. 2, 457–486 (1997; Zbl 0891.03029)], which implies a lower bound for a variant of clique/color tautologies with respect to OBDD refutations using a specific ordering of the variables. The author then applies a substitution, which has the effect of introducing a permutation of input variables, and obtains an exponential lower bound on arbitrary OBDD refutations.

MSC:
03F20 Complexity of proofs
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