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Exact phase transitions in random constraint satisfaction problems. (English) Zbl 0940.68099
Summary: 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.

68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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