On the power of one-way communication
Journal of the ACM (JACM)
Garden of Eden configurations for cellular automata on Cayley graphs of groups
SIAM Journal on Discrete Mathematics
One-way cellular automata on Cayley graphs
Theoretical Computer Science
The growth rate of vertex-transitive planar graphs
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
NP problems are tractable in the space of cellular automata in the hyperbolic plane
Theoretical Computer Science
Fast one-way cellular automata
Theoretical Computer Science - Mathematical foundations of computer science
Cellular Automata
Changing the neighborhood of cellular automata
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
How does the neighborhood affect the global behavior of cellular automata?
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
Hi-index | 0.00 |
In a previous paper we formulated and analyzed the structure ofneighborhoods of cellular automata in an algebraic setting suchthat the cellular space S is represented by the Cayley graph of afinitely generated group and the neighbors are defined as asemigroup generated by the neighborhood N as a subset of S, Nishioand Margenstern 2004 [14,15]. Particularly we discussed the horsepower problem whether the motion of a horse (knight) fills theinfinite chess board or Z^2 - that is, an algebraic problem whethera subset of a group generates it or not. Among others we provedthat a horse fills Z^2 even when its move is restricted to properlychosen 3 directions and gave a necessary and sufficient conditionfor a generalized 3-horse to fill Z^2. This paper gives furtherdevelopments of the horse power problem, say, on the higherdimensional Euclidean grid, the hexagonal grid and the hyperbolicplane.