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 …

We describe a general method to obtain quantum speedups of classical algorithms which
are based on the technique of backtracking, a standard approach for solving constraint …

Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied
clauses in a CNF formula. We propose a resolution-like calculus for Max-SAT and prove its …

Research in algorithms for Boolean satisfiability and their implementations [23, 6] has
recently outpaced benchmarking efforts. Most of the classic DIMACS benchmarks [10] can …

Research in algorithms for Boolean satisfiability (SAT) and their implementations (Goldberg
and Novikov, 2002),(Moskewicz et al., 2001),(Silva and Sakallah, 1999) has recently …

This paper analyzes the resolution complexity of two random constraint satisfaction problem
(CSP) models (ie Model RB/RD) for which we can establish the existence of phase …

Let P be a k-ary predicate over a finite alphabet. Consider a random CSP (P) instance I over
n variables with m constraints. When m≫ n the instance will be unsatisfiable with high …

Propositional proof complexity is the study of the sizes of propositional proofs, and more
generally, the resources necessary to certify propositional tautologies. Questions about …

An active line of research in proof complexity over the last decade has been the study of
proof space and trade-offs between size and space. Such questions were originally …

We prove a new switching lemma that works for restrictions that set only a small fraction of
the variables and is applicable to formulas in disjunctive normal form (DNFs) with small …