Abstract
Since their introduction, Boolean networks have been traditionally studied in view of theirrich dynamical behaviour under different update protocols and for their qualitative analogywith cell regulatory networks. More recently, tools borrowed from the statistical physics ofdisordered systems and from computer science have provided a more completecharacterization of their equilibrium behaviour. However, the largest numberof results have been obtained in the thermodynamic limit, which is often farfrom being reached when dealing with realistic instances of the problem. Thenumerical analysis presented here aims at comparing—for a specific family ofmodels—the outcomes given by the heuristic belief propagation algorithm withthose given by exhaustive enumeration. In the second part of the paper someanalytical considerations on the validity of the annealed approximation are discussed.
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