§ 1. Introduction. The classical propositional calculus has an undeserved reputation among
logicians as being essentially trivial. I hope to convince the reader that it presents some of …

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 …

Staff View: Bounded Arithmetic and Resolution-Based Proof Systems Swansea University
Logo THE UNIVERSITY RESEARCH UNDERGRADUATE POST GRADUATE …

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 …

This thesis is dedicated to the study of the relations between uniform and nonuniform proof
complexity and computational complexity. Nonuniform proof complexity studies the lengths …

This is a survey of basic facts about bounded arithmetic and about the relationships between
bounded arithmetic and propositional proof complexity. We introduce the theories and of …

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 …

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 …

A possibly unexpected by-product of the mathematical study of the lengths of proofs, as is
done in the field of propositional proof complexity, is, I claim, that it may lead to new …

In many parts of mathematics one finds statements asserting that a finite object with a
particular, feasibly verifiable, property does not exist. Such statements include, for example …