Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler-Leman Refinement Steps

Electronic Colloquium on Computational Complexity (ECCC), Volume abs/1608.08704, 2016, Pages 267-276.

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Abstract:

We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every such sentence requires quantifier depth at least nΩ(k / log k). Our trade-offs also apply to first-order counting l...More

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