Emergence in SAT Problems: Critical Thresholds under Constraint Density
Abstract
The SAT problem is a central NP-complete problem. This study experimentally explores whether a critical threshold-an emergence point-exists where the satisfiability of 3-SAT instances changes sharply as constraints increase. By generating thousands of random instances and measuring satisfiability and solving time across varying constraint densities (r = m/n), we observed a phase-transition-like behavior. This approach offers a new perspective on NP problems, linking them with emergence phenomena in complex systems.