Supercritical Space-Width Trade-offs for Resolution

Christoph Berkholz; Jakob Nordström

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arXiv · 1612.07162

Supercritical Space-Width Trade-offs for Resolution

Christoph Berkholz·Jakob Nordström

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Abstract

We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the space-width trade-offs in [Ben-Sasson '09]}, and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [Razborov '16]. We obtain our results by using Razborov's new hardness condensation technique and combining it with the space lower bounds in [Ben-Sasson and Nordstrom '08].

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Christoph Berkholz, Jakob Nordström. 2016-12-21. Supercritical Space-Width Trade-offs for Resolution. https://arxiv.org/abs/1612.07162

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