Let F be a function from {0, 1}n into itself whose components are symmetric threshold functions. We introduce a monotonic operator, analogous to the spin glass energy [1], [9], to compare the… (More)

The dynamics of several games on line graphs is studied. Relations between these games and a one-dimensional version of the sand pile model are established. We also study a generalization of the… (More)

In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of LB, lattice of integer partitions introduced in… (More)

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which… (More)

We exhibit a class of symmetric neural networks which synchronous iteration possesses an exponential t ransient length. In fact if {I , ... , n} is the set of nodes we prove the transient length… (More)

The virtual ant introduced by Langton [Physica D 22 (1986) 120] has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit… (More)

Number-conserving (or conservative) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In… (More)