Cellular Automata: Real-Time Equivalence Between One-Dimensional Neighborhoods

Abstract. It is well known that one-dimensional cellular automata working on the usual neighborhood are Turing complete, and many acceleration theorems are known. However very little is known about the other neighborhoods. In this article, we prove that every one-dimensional neighborhood that is sufficient to recognize every Turing language is equivalent (in terms of real-time recognition) either to the usual neighborhood {−1, 0, 1} or to the one-way neighborhood {0, 1}.

• Type: Conference
• Year: 2005
• Where: STACS
• Authors: Victor Poupet
• Keywords: One-dimensional Cellular Automata, One-dimensional Neighborhood, STACS 2005, Theoretical Computer Science, Usual Neighborhood