Renormalization group approach to satisfiability

Department of Physics, University of Wisconsin - 1150 University Avenue, Madison, WI 53706, USA

Received: 3 July 2006
Accepted: 11 December 2006

Abstract

Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical ORs of these variables is true. Here, a renormalization group transformation is constructed and used to relate the properties of satisfiability problems with different numbers of variables in each clause. The transformation yields new insight into phase transitions delineating “hard” and “easy” satisfiability problems.