Constant acceleration theorem for extended von neumann neighbourhoods

Abstract

We study 2-dimensional cellular automata as language recognizers. We are looking for closure properties, similar to the one existing in one dimension. Some results are already known for the most used neighbourhoods, however many problems remain open concerning more general neighbourhoods. In this paper we provide a construction to prove a constant acceleration theorem for extended von Neumann neighbourhoods. We then use this theorem and some classical tools to prove the equivalence of those neighbourhoods, considering the set of languages recognizable in real time.