## Are there Hard Examples for Frege Systems?

Citations: | 20 - 2 self |

### BibTeX

@MISC{Bonet_arethere,

author = {Maria Luisa Bonet and Samuel R. Buss and Toniann Pitassi},

title = {Are there Hard Examples for Frege Systems?},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

It is generally conjectured that there is an exponential separation between Frege and extended Frege systems. This paper reviews and introduces some candidates for families of combinatorial tautologies for which Frege proofs might need to be superpolynomially longer than extended Frege proofs. Surprisingly, we conclude that no particularly good or convincing examples are known. The examples of combinatorial tautologies that we consider seem to give at most a quasipolynomial speed-up of extended Frege proofs over Frege proofs, with the sole possible exception of tautologies based on a theorem of Frankl. It is