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Paper:

TR25-116 | 28th July 2025 10:43

Supercritical Tradeoff Between Size and Depth for Resolution over Parities

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Abstract:

Alekseev and Itsykson (STOC 2025) proved the existence of an unsatisfiable CNF formula such that any resolution over parities (Res($\oplus$)) refutation must either have exponential size (in the formula size) or superlinear depth (in the number of variables). In this paper, we extend this result by constructing a formula with the same hardness properties, but which additionally admits a resolution refutation of quasi-polynomial size. This establishes a supercritical tradeoff between size and depth for resolution over parities.

The proof builds on the framework of Alekseev and Itsykson and relies on a lifting argument applied to the supercritical tradeoff between width and depth in resolution, proposed by Buss and Thapen (IPL 2026).



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