Bose-Einstein Condensation in Satisfiability Problems

TL;DR

This paper introduces a novel physics-inspired approach to analyze satisfiability problems, revealing phase transitions akin to Bose-Einstein condensation, and improves SAT solver performance using this insight.

Contribution

It presents a new statistical physics-based characterization of k-SAT, linking network phase transitions to Bose-Einstein condensation, and enhances SAT solvers with this understanding.

Findings

k-SAT networks follow Bose statistics

Phase transition in k-SAT correlates with Bose-Einstein condensation

Enhanced SAT solver performance using fitness-based classification

Abstract

This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose-Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose-Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose-Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools.