Synchronous Networks Over Finite Fields

Abstract

This paper investigates the synchronization problem of networks over finite fields. Firstly, based on the finite-field synchronizable (FFS) property of matrices, a necessary and sufficient condition is derived for finite-field synchronous networks. Then, the inverse recursion subspaces of networks over finite fields are studied. It is revealed that the synchronization of finite-field networks can be determined by a fraction of states. Finally, as an application, the obtained results are generalized to a class of Boolean networks.