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QUASIPOLYNOMIAL SIZE FREGE PROOFS OF FRANKL’S THEOREM ON THE TRACE OF SETS

Published online by Cambridge University Press:  10 May 2016

JAMES AISENBERG ,
MARIA LUISA BONET  and
SAM BUSS
JAMES AISENBERG
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA SAN DIEGO, LA JOLLA CA 92093-0112, USAEmail:jaisenberg@math.ucsd.edu
MARIA LUISA BONET
Affiliation:
LENGUAJES Y SISTEMAS INFORMÁTICOS UNIVERSIDAD POLITÉCNICA DE CATALUÑA BARCELONA, SPAINEmail: bonet@lsi.upc.edu
SAM BUSS
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA SAN DIEGO, LA JOLLA CA 92093-0112, USAEmail: sbuss@math.ucsd.edu
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Abstract

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 parameter t, we prove that Frankl’s Theorem has polynomial size AC0-Frege proofs from instances of the pigeonhole principle.

Keywords

Frege proofsextended Frege proofsFrankl’s theoremtrace of setsKruskal–Katona theoremhereditary matrix
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 687 - 710
Copyright
Copyright © The Association for Symbolic Logic 2016 

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