Amalgamation of cellular automata

In this paper, we study amalgamations of cellular automata (CA), i.e. ways of combining two CA by disjoint union. We show that for several families of CA obtained by simple amalgamation operations (including the well-known families of majority and minority CA), the density of a large class of properties follows a zero-one law. Besides, we establish that intrinsic universality in those families is always non-trivial and undecidable for some of them. Therefore we obtain various syntactical means to produce CA which are almost all intrinsically universal. These results extend properties already obtained for captive cellular automata. We additionally prove that there exists some reversible captive CA which are (intrinsically) universal for reversible CA.

• Type: Conference
• Year: 2008
• Where: JAC
• Authors: Guillaume Theyssier
• Keywords: Artificial Intelligence, Cellular Automata, JAC 2008, Minority Ca, Reversible Captive Ca