Non-Automatizability of Bounded-Depth Frege Proofs

Abstract.In this paper, we show how to extend the argument due to Bonet, Pitassi and Raz to show that bounded-depth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the Diffie–Hellman function is sufficiently hard. It follows as a corollary that bounded-depth Frege is not automatizable; in other words, there is no deterministic polynomial-time algorithm that will output a short proof if one exists. A notable feature of our argument is its simplicity.

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