Abstract
We prove an exponential lower bound for the length of any resolution proof for the same set of clauses as the one used by Urquhart [13]. Our contribution is a significant simplification in the proof and strengthening of the bound, as compared to [13]. We use on the one hand a simplification similar to the one suggested by Beame and Pitassi in [1] for the case of the pidgeon hole clauses. Additionally, we base our construction on a simpler version of expander graphs than the ones used in [13]. These expander graphs are located in the core of the construction. We show the existence of our expanders by a Kolmogorov complexity argument which has not been used before in this context and might be of independent interest since the applicability of this method is quite general.
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References
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© 1997 Springer-Verlag Berlin Heidelberg
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Schöning, U. (1997). Resolution proofs, exponential bounds, and Kolmogorov complexity. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029954
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DOI: https://doi.org/10.1007/BFb0029954
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