Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have
published seminal works by leading logicians. Many of the original books in the series have …

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for
nonspecialists. There is a strong emphasis on theorems with particularly elegant and …

Boolean circuit complexity is the combinatorics of computer science and involves many
intriguing problems that are easy to state and explain, even for the layman. This book is a …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

Abstract The Pigeonhole Principle for n is the statement that there is no one-to-one function
between a set of size n and a set of size n− 1. This statement can be formulated as an …

This account of propositional logic concentrates on the algorithmic translation of important
methods, especially of decision procedures for (subclasses of) propositional logic. Important …

This chapter gives an overview of proof complexity and connections to SAT solving, focusing
on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes …

§ 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 …

In this paper we prove an exponential lower bound on the size of bounded-depth Frege
proofs for the pigeonhole principle (PHP). We also obtain an Ω (loglog n)-depth lower bound …

The method of analytic tableaux is a direct descendant of Gentzen's cut-free sequent
calculus and is regarded as a paradigm of the notion of analytic deduction in classical logic …