Threshold Behavior in a Boolean Network Model for SAT

Boolean satisfiability (SAT) is the canonical NP-complete problem that plays an important role in AI and has many practical applications in Computer Science in general. Boolean networks (BN) are dynamical systems that have recently been proposed as an algorithm for solving SAT problems [7]. We have carried out a detailed investigation of the dynamical properties of BN corresponding to random SAT problems of different size. We varied the problem size by changing the number of variables and the number of clauses in the Boolean formula. We show that dynamics of BN corresponding to 3-SAT problems display a threshold-like behavior, although this transition occurs far below the well known phase transition in the computational complexity of random 3-SAT. This threshold behavior does not appear to be connected to the transition between frozen and chaotic dynamics regimes of random BN.

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