Guest Column Page 1 Guest Column: Proof Complexity and Beyond1 Alexander Razborov2
Abstract This essay is a highly personal and biased account of some main concepts and …

The basic task of propositional proof complexity is to learn as much as possible about the
behavior of SP (φ) for “interesting” proof systems P and “interesting” tautologies φ. In …

We exhibit an unusually strong tradeoff in propositional proof complexity that significantly
deviates from the established pattern of almost all results of this kind. Namely, restrictions on …

This article is an abridged and revised version of a 1996 McGill University technical report
[15]. The technical report was based on lectures delivered by the author at a workshop in …

Proof complexity, the study of the lengths of proofs in propositional logic, is an area of study
that is fundamentally connected both to major open questions of computational complexity …

We exhibit an unusually strong trade-off between resolution proof width and tree-like proof
size. Namely, we show that for any parameter k= k (n) there are unsatisfiable k-CNFs that …

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 …

This book treats bounded arithmetic and propositional proof complexity from the point of
view of computational complexity. The first seven chapters include the necessary logical …

When I was an undergraduate, I fell in love with propositional logic (strange as this may
seem to the countless students I have tortured with tough logic problems in tests and …

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 …