Non-automatizability of bounded-depth frege proofs

Authors:
Maria Luisa Bonet;Carlos Domingo;Ricard Gavaldà;Alexis Maciel;Toniann Pitassi
Affiliations:
Department of Software (LSI) Universitat Politècnica de Catalunya, Barcelona, Spain;Department of Mathematical and Computing Science, Tokoyo Institute of Technology, Ookayama, Meguro-ko, Tokoyo, Japan;Department of Software (LSI), Univesitat Politècnica de Catalunya, Barcelona, Spain;Department of Mathematics and Computer Science, Clarkson University, Postdam, NY;Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, M5S 3G4
Venue:
Computational Complexity
Year:
2004

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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.