Core percolation and onset of complexity in boolean networks.

The determination and classification of fixed points of large Boolean networks is addressed in terms of a constraint-satisfaction problem. We develop a general simplification scheme that, removing all those variables and functions belonging to trivial logical cascades, returns the computational core of the network. The transition line from an easy to a complex regulatory phase is described as a function of the parameters of the model, identifying thereby both theoretically and algorithmically the relevant regulatory variables.

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