This note, based on my 4ECM lecture, exposes few basic points of proof complexity in a way
accessible to any mathematician. In many parts of mathematics one finds statements …

We show that an LK proof of size m of a monotone sequent (a sequent that contains only
formulas in the basis∧,∨) can be turned into a proof containing only monotone formulas of …

We study Frege proofs for the one-to-one graph Pigeon Hole Principle defined on the n*n
grid where n is odd. We are interested in the case where each formula in the proof is a depth …

We construct quasipolynomial-size proofs of the propositional pigeonhole principle in the
deep inference system KS, addressing an open problem raised in previous works and …

We give a combinatorial analysis (using edge expansion) of a variant of the iterative
expander construction due to Reingold, Vadhan, and Wigderson [44], and show that this …

In this paper we investigate two properties of some propositional systems of Intuitionistic,
Johansson's and Monotone logics: 1) the relations between the proofs complexities of …

In this work we investigate 1) the relations between the proofs complexities of strongly equal
tautologies and 2) the relations between the proofs complexities of minimal tautologies and …

Abstract Atserias, Galesi, and Pudlák have shown that the monotone sequent calculus MLK
quasipolynomially simulates proofs of monotone sequents in the full sequent calculus LK (or …

1. Введение. Традиционно считалось, что минимальные тавтологии, т. е. тавтологии,
которые не являются результатом подстановки в более короткие тавтологии, не могут …

We develop approximate counting of sets definable by Boolean circuits in bounded
arithmetic using the dual weak pigeonhole principle (sWPHP (PV)), as a generalization of …