Parallel and Sequential Computation on Boolean Networks

Abstract A model of large assemblies of computing elements is provided by the concept of boolean network F :{0, 1} n → {0, 1} n . Then we compare different regimes of this system, namely, parallel and sequential computations within the framework of discrete iterations. It is shown that, although the asymptotic behavior of the network—as characterized by the limit cycles of the iterations—may differ from one sort of regime to another, it may, however, be largely predicted as for its spatial structure. We show that for all iterations some elements never change state in any limit cycle: they form the stable core. We introduce the notion of forcing domain of a boolean network, provide an algorithm to build it and show that it is a good approximation to the stable core. This, thus, provides a spatial characterization of the limit cycles of the different iterations. A theoretical bound on the transient length is provided through the entropy of the network.