Captive Cellular Automata

Abstract. We introduce a natural class of cellular automata characterised by a property of the local transition law without any assumption on the states set. We investigate some algebraic properties of the class and show that it contains intrinsically universal cellular automata. In addition we show that Rice’s theorem for limit sets is no longer true for that class, although infinitely many properties of limit sets are still undecidable. Cellular automata (ca for short) are discrete dynamical systems capable of producing a wide class of different behaviours. They consist of a large collection of simple identical components (the cells) with uniform local interactions. As such they provide an idealistic model to study complex systems observed in nature. Despite the simplicity of the model, most of the richness of behaviours they exhibit is still to be understood. Moreover, many interesting and natural properties are undecidable. To that extent it is meaningful to consider classes of...

• Type: Conference
• Year: 2004
• Where: MFCS
• Authors: Guillaume Theyssier
• Keywords: Cellular Automata, Local Transition Law, MFCS 2004, Universal Cellular Automata