The Moore-Myhill pseudo tiling for the Heisenberg tessellation automata
- Shûichi Yukita
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The notions of a Garden-of-Eden (GOE) configuration and mutually erasable configurations were discovered and investigated in the framework of Euclidean tessellations in the 1960s and 1970s. In 1993, Machi and Mignosi extended the GOE theorem for tessellation automata on Cayley graphs of non-exponential growth. We give an alternative proof to the GOE theorem for the discrete Heisenberg groups. Our proof has the advantage that it fully exploits the particular group structure so that a Moore-Myhill like tiling can be explicitly constructed. The tiling, as the wording suggests, is a spatially economic covering. The non-uniform packing method is introduced as a key technique for the construction.
- G.C.S. Amoroso and Y. Patt, Some clarifications of the concept of a Garden-of-Eden configuration. J. Computer and System Sciences,10 (1975), 77–82.
- M. Garzon, Models of Massive Parallelism, Springer, 1995.
- A. Machì and F. Mignosi, Garden of Eden configurations for cellular automata on Cayley graphs of groups. SIAM J. Discrete Math.,6 (1993), 44–56. CrossRef
- E.F. Moore, Machine models of self-reproduction. Proceedings of a Symposium of the Applied Mathematical Society, Providence, R.I., 1962, 17–33.
- J. Myhill, The converse to Moore’s Garden-of-Eden theorem. Proc. Amer. Math. Soc,14 (1963), 685–686. CrossRef
- J. Von Neumann, Theory of Self-reproducing Automata (Edited and completed by A.W. Burks). Univ. of Illinois Press, Urbana, 1966.
- S. Yukita, Tessellation automata on free groups. Hiroshima Math. J.,25 (1995), 561–570. (first appeared as a Tech. Rep. 94-1-044, Department of Computer Software, The University of Aizu, 1994.)
- S. Yukita, Tessellation automata on Fuchsian groups. Tech. Rep. 94-1-045, Department of Computer Software, The University of Aizu, 1994.
- The Moore-Myhill pseudo tiling for the Heisenberg tessellation automata
Japan Journal of Industrial and Applied Mathematics
Volume 16, Issue 1 , pp 47-63
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- tessellation automata
- Heisenberg groups
- Garden-of-Eden theorem
- non-Euclidean tessellation
- Moore-Myhill pseudo tiling
- Shûichi Yukita (1)
- Author Affiliations
- 1. Department of Computer Software, The University of Aizu, 965- 8580, Fukushima, Japan