Quasipolynomial size Frege proofs of frankl’s theorem on the trace of sets

Journal of Symbolic Logic 81 (2):687-710 (2016)
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We extend results of Bonet, Buss and Pitassi on Bondy’s Theorem and of Nozaki, Arai and Arai on Bollobás’ Theorem by proving that Frankl’s Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parametert, we prove that Frankl’s Theorem has polynomial size AC0-Frege proofs from instances of the pigeonhole principle.



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Propositional Consistency Proofs.Samuel R. Buss - 1991 - Annals of Pure and Applied Logic 52 (1-2):3-29.

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