On ACC0[pk] Frege proofs

We show that for every prime power pk , quasipolynomiaf size bounded-depth Frege proofs with mod pk counting comectives can be simulated by quasipolynomiaf-size proofs of depth 3 consisting of a threshold connective at the output, mod pk connective on level two, and AND connective of small fan-in on level one. We argue that this result is a plausible first step towards proving lower bounds for bounded-depth Frege proofs with modular connective, an outstanding open problem. We also discuss possible int cresting consequences for automated theorem proving.

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