A simplified way of proving trade-off results for resolution

Authors:
Jakob Nordström
Affiliations:
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Information Processing Letters
Year:
2009

Citing 12
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Abstract

We present a greatly simplified proof of the length-space trade-off result for resolution in [P. Hertel, T. Pitassi, Exponential time/space speedups for resolution and the PSPACE-completeness of black-white pebbling, in: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS '07), Oct. 2007, pp. 137-149], and also prove a couple of other theorems in the same vein. We point out two important ingredients needed for our proofs to work, and discuss some possible conclusions. Our key trick is to look at formulas of the type F=G@?H, where G and H are over disjoint sets of variables and have very different length-space properties with respect to resolution.