Exact Phase Transitions in Random Constraint Satisfaction Problems

TL;DR

This paper introduces Model RB, a new random CSP model, proving the existence and exact location of phase transitions from satisfiable to unsatisfiable problems as variables grow large.

Contribution

It presents a revised CSP model with proven phase transition points and links its hardness to existing models, highlighting the presence of many hard instances.

Findings

Phase transitions exist in Model RB as variables approach infinity.

Exact critical values for phase transitions are determined.

Model RB contains many hard instances similar to Model B.

Abstract

In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all problems are unsatisfiable do exist for Model RB as the number of variables approaches infinity. Moreover, the critical values at which the phase transitions occur are also known exactly. By relating the hardness of Model RB to Model B, it is shown that there exist a lot of hard instances in Model RB.