Issue
EPL
Volume 77, Number 3, February 2007
Article Number 30006
Number of page(s) 4
Section General
DOI http://dx.doi.org/10.1209/0295-5075/77/30006
Published online 02 February 2007
EPL, 77 (2007) 30006
DOI: 10.1209/0295-5075/77/30006

Renormalization group approach to satisfiability

S. N. Coppersmith

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


received 3 July 2006; accepted in final form 11 December 2006; published February 2007
published online 2 February 2007

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.

PACS
05.10.Cc - Renormalization group methods.
89.20 Ff - Computer science and technology.
75.10.Nr - Spin-glass and other random models.

© Europhysics Letters Association 2007