Renormalization group approach to satisfiability

TL;DR

This paper applies a renormalization group method to satisfiability problems, revealing phase transitions that distinguish between hard and easy instances, and relating properties across different clause sizes.

Contribution

It introduces a novel renormalization group transformation for satisfiability problems, providing new insights into their phase transition behavior.

Findings

Identifies phase transitions between hard and easy satisfiability problems.

Relates properties of satisfiability problems with different clause sizes.

Provides a new analytical framework for understanding computational complexity in SAT.

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 OR's 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.