Exact phase transitions in random constraint satisfaction problems

Authors:
Ke Xu;Wei Li
Affiliations:
National Laboratory of Software Development Environment, Department of Computer Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China;National Laboratory of Software Development Environment, Department of Computer Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China
Venue:
Journal of Artificial Intelligence Research
Year:
2000

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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.