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- W4313203208 abstract "We study Frege proofs using depth-d Boolean formulas for the Tseitin contradiction on $ntimes n$ grids. We prove that if each line in the proof is of size M then the number of lines is exponential in $n/(log M)^{O(d)}$. This strengthens a recent result of Pitassi et al. [12]. The key technical step is a multi-switching lemma extending the switching lemma of Hastad [8] for a space of restrictions related to the Tseitin contradiction. The strengthened lemma also allows us to improve the lower bound for standard proof size of bounded depth Frege refutations from exponential in $tilde{Omega}(n^{1/59d})$ to exponential in $tilde{Omega}(n^{1/(2d-1)})$." @default.
- W4313203208 created "2023-01-06" @default.
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- W4313203208 date "2022-10-01" @default.
- W4313203208 modified "2023-10-16" @default.
- W4313203208 title "On Bounded Depth Proofs for Tseitin Formulas on the Grid; Revisited" @default.
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- W4313203208 doi "https://doi.org/10.1109/focs54457.2022.00110" @default.
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