Abstract
We give the first time-space trade-off 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 size (and space) $T(N)= N^{\Theta(\log N)}$ (and like all formulas have another resolution refutation of space $N$) but for which no resolution refutation can simultaneously have space $S(N) = T(N)^{o(1)}$ and size $T(N)^{O(1)}$. In other words, any substantial reduction in space results in a super-polynomial increase in total size. We also show somewhat stronger time-space trade-off lower bounds for regular resolution, which are also the first to apply to superlinear space. For any function $T$ that is at most weakly exponential, $T(N) = 2^{o(N^{1/4})}$, we give a tautology that has regular resolution proofs of size and space $T(N)$, but no such proofs with space $S(N) = T(N)^{1-\Omega(1)}$ and size $T(N)^{O(1)}$. Thus, any polynomial reduction in space has a superpolynomial cost in size. These tautologies...
Published Version
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