Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra
and computer science. This self-contained book presents the basic concepts, classical …

We obtain two results about the proof complexity of deep inference:(1) Deep-inference proof
systems are as powerful as Frege ones, even when both are extended with the Tseitin …

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 introduce a more general notion of efficient simulation between proof systems, which we
call effectively-p simulation. We argue that this notion is more natural from a complexity …

Atomic flows are a geometric invariant of classical propositional proofs in deep inference. In
this thesis we use atomic flows to describe new normal forms of proofs, of which the …

We investigate the substitution Frege (SF) proof system and its relationship to extended
Frege (EF) in the context of modal and superintuitionistic (si) propositional logics. We show …

We investigate the proof complexity of analytic subsystems of the deep inference proof
system SKSg (the calculus of structures). Exploiting the fact that the cut rule (i↑) of SKSg …

We show that strong-enough lower bounds on monotone arithmetic circuits or the
nonnegative rank of a matrix imply unconditional lower bounds in arithmetic or Boolean …

Jeřábek showed in 2008 that cuts in propositional-logic deep-inference proofs can be
eliminated in quasipolynomial time. The proof is an indirect one relying on a result of …

Does every Boolean tautology have a short propositional-calculus proof? Here, a
propositional-calculus (ie, Frege) proof is any proof starting from a set of axioms and …