Resolution and binary decision diagrams cannot simulate each other polynomially

Authors:
J. F. Groote;H. Zantema
Affiliations:
Department of Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Discrete Applied Mathematics - The renesse issue on satisfiability
Year:
2003

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Abstract

There are many different ways of proving formulas in propositional logic. Many of these can easily be characterized as forms of resolution. Others use so-called binary decision diagrams (BDDs). Experimental evidence suggests that BDDs and resolution-based techniques are fundamentally different, in the sense that their performance can differ very much on benchmarks. In this paper, we confirm these findings by mathematical proof. We provide examples that are easy for BDDs and exponentially hard for any form of resolution, and vice versa, examples that are easy for resolution and exponentially hard for BDDs.