Paper Info
Title
Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space
Abstract
We give the first time-space tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Resolution refutations of space and size each roughly Nlog2 N (and like all formulas have Resolution refutations of space N) for which any Resolution refutation using space S and length T requires T ≥ (N0.58 log2 N/S)Ω(log log N/log log log N). By downward translation, a similar tradeoff applies to all smaller space bounds. We also show somewhat stronger time-space tradeoff lower bounds for Regular Resolution, which are also the first to apply to superlinear space. Namely, for any space bound S at most 2o(N1/4) there are formulas of size $N$, having clauses of width 4, that have Regular Resolution proofs of space S and slightly larger size T=O(NS), but for which any Regular Resolution proof of space S1-ε requires length TΩ(log log N/ log log log N).
Year
DOI
Venue
2011
10.1145/2213977.2213999
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Keywords
DocType
Citations 
log log n,resolution refutation,smaller space bound,regular resolution proof,time-space tradeoffs,log2 n,nlog2 n,superlinear space,size n,log log log n,lower bound,space n,proof complexity
Journal
20
PageRank 
References 
Authors
0.67
22
3
Name
Order
Citations
PageRank
Paul Beame12234176.07
Christopher Beck2271.53
Russell Impagliazzo35444482.13