Quasipolynomial size frege proofs of Frankl's Theorem on the trace of sets

We extend results of Bonet, Buss and Pitassi on Bondy's Theorem and of Nozaki, Arai and Arai on Bollobas' 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 AC(0)-Frege proofs from instances of the pigeonhole principle.Peer ReviewedPostprint (author's final draft

2-D Tucker is PPA complete

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k≥2. This corrects a claim in the literature that the Tucker search problem is in PPAD.Peer ReviewedPostprint (author's final draft

Short proofs of the Kneser-Lovász coloring principle

We prove that propositional translations of the Kneser–Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs for all fixed values of k. We present a new counting-based combinatorial proof of the K neser–Lovász theorem based on the Hilton–Milner theorem; this avoids the topological arguments of prior proofs for all but finitely many base cases. We introduce new “truncated Tucker lemma” principles, which are miniaturizations of the octahedral Tucker lemma. The truncated Tucker lemma implies the Kneser–Lovász theorem. We show that the k=1 case of the truncated Tucker lemma has polynomial size extended Frege proofs.Peer ReviewedPostprint (author's final draft

Regionalização para o cultivo do feijão no Rio Grande do Sul com base na interação genótipo x ambiente¹.

bitstream/item/59171/1/Iraja-V59N002P19810.pd