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Details for article 4 of 7 found articles
| Title: |
On Algebraic Structure of Neighborhoods of Cellular AutomataHorse Power Problem |
| Author: |
Nishio, Hidenosuke Margenstern, Maurice von Haeseler, Friedrich |
| Appeared in: |
Fundamenta informaticae |
| Paging: | Volume 78 (2007) nr. 3 pages 397-416 |
| Year: |
2007-08-22 |
| Contents: |
In a previous paper we formulated and analyzed the structure of neighborhoods of cellular automata in an algebraic setting such that the cellular space S is represented by the Cayley graph of a finitely generated group and the neighbors are defined as a semigroup generated by the neighborhood N as a subset of S, Nishio and Margenstern 2004 [14,15]. Particularly we discussed the horse power problem whether the motion of a horse (knight) fills the infinite chess board or Z^2 – that is, an algebraic problem whether a subset of a group generates it or not. Among others we proved that a horse fills Z^2 even when its move is restricted to properly chosen 3 directions and gave a necessary and sufficient condition for a generalized 3-horse to fill Z^2. This paper gives further developments of the horse power problem, say, on the higher dimensional Euclidean grid, the hexagonal grid and the hyperbolic plane. |
| Publisher: |
IOS Press |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 4 of 7 found articles
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