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

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

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.

Maurice Margenstern

[1] Maurice Margenstern,et al. A universal cellular automaton on the heptagrid of the hyperbolic plane with four states , 2011, Theor. Comput. Sci..

[2] Turlough Neary,et al. Four Small Universal Turing Machines , 2009, Fundam. Informaticae.

[3] Maurice Margenstern,et al. New Tools for Cellular Automata in the Hyperbolic Plane , 2000, J. Univers. Comput. Sci..

[4] Maurice Margenstern. Cellular Automata in Hyperbolic Spaces , 2009, Encyclopedia of Complexity and Systems Science.

[5] Mats G. Nordahl,et al. Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[6] Maurice Margenstern. About the embedding of one dimensional cellular automata into hyperbolic cellular automata , 2010, ArXiv.

[7] Raphael M. Robinson,et al. MINSKY'S SMALL UNIVERSAL TURING MACHINE , 1991 .