"Planar" Tautologies Hard for Resolution

Authors:
Sren Riis
Affiliations:
-
Venue:
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Year:
2001

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Abstract

We prove exponential lower bounds on the resolution proofs of some tautologies, based on rectangular grid graphs. More specifically, we show a 2^{\Omega (n)} lower bound for any resolution proof of the mutilated chessboard problem on a 2n 脳 2n chessboard as well as for the Tseitin tautology based on the n 脳 n rectangular grid graph. The former result answers a 35 year old conjecture by McCarthy.