An Upper Bound on the Number of States for a Strongly Universal Hyperbolic Cellular Automaton on the Pentagrid

Maurice Margenstern (1)

1 LITA - Laboratoire d'Informatique Théorique et Appliquée

In this paper, following the way opened by a previous paper deposited on arXiv, we give an upper bound to the number of states for a hyperbolic cellular automaton in the pentagrid. Indeed, we prove that there is a hyperbolic cellular automaton which is rotation invariant and whose halting problem is undecidable and which has 9 states.

Keywords: cellular automata; strong universality; hyperbolic spaces; tilings

Domains: Other [cs.OH]

Maurice Margenstern. An Upper Bound on the Number of States for a Strongly Universal Hyperbolic Cellular Automaton on the Pentagrid. Journées Automates Cellulaires 2010, Dec 2010, Turku, Finland. pp.168-179. ⟨hal-00541965⟩