Predecessors and Garden-of-Eden configurations in parallel dynamical systems on maxterm and minterm Boolean functions

Abstract

In this work, we solve the classical predecessor problems for parallel dynamical systems on maxterm and minterm Boolean functions. Actually, we solve analytically the predecessor existence problem by giving a characterization to have a predecessor for any given configuration. As a consequence, we also get a characterization of the Garden-of-Eden configurations of these systems. Moreover, the structure of the predecessors found out allows us to give a solution to the unique predecessor problem , the coexistence of predecessors problem and the number of predecessors problem .