Exponential Separation of Res(k) and Res(k+1)

Sam Buss, Russell Impagliazzo and Nathan Segerlind
January 11, 2002

For each k >= 1, we give a famiily of unsatisfiable sets of clauses which have polynomial size {\mbox{Res}}(k+1) refutations, but which require {\mbox{Res}}(k) refutations of 2^{n^{\epsilon_k}}. This improves the superpolynomial- separation between resolution and {\mbox{Res}}(2) given by Bonet and Galesi to exponential. As a corollary, we obtain an exponential separation between depth 0 Frege and depth 1 Frege, improving upon the superpolynomial separation given by the weak pigeonhole principle.

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