Geodesic
On Finite State Automation of 4 Stones which Makes the
Matematičeskoe obrazovanie, no. 1 (2016), pp. 23-43
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A finite state automation of 4 stones is constructed to make the round of $\mathbb{Z}^k$ for a polynomial time. Some estimates of the optimal number of stones are discussed.
Keywords: The state machine, stone, crawling $k$-dimensional space, polynomial time visiting points. 
@article{MO_2016_1_a4,
     author = {D. V. Gusev},
     title = {On {Finite} {State} {Automation} of 4 {Stones} which {Makes} the},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {23--43},
     year = {2016},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2016_1_a4/}
}
TY  - JOUR
AU  - D. V. Gusev
TI  - On Finite State Automation of 4 Stones which Makes the
JO  - Matematičeskoe obrazovanie
PY  - 2016
SP  - 23
EP  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MO_2016_1_a4/
LA  - ru
ID  - MO_2016_1_a4
ER  - 
%0 Journal Article
%A D. V. Gusev
%T On Finite State Automation of 4 Stones which Makes the
%J Matematičeskoe obrazovanie
%D 2016
%P 23-43
%N 1
%U http://geodesic.mathdoc.fr/item/MO_2016_1_a4/
%G ru
%F MO_2016_1_a4
D. V. Gusev. On Finite State Automation of 4 Stones which Makes the. Matematičeskoe obrazovanie, no. 1 (2016), pp. 23-43. http://geodesic.mathdoc.fr/item/MO_2016_1_a4/

[1] Kudryavtsev V.B., Aleshin S.V., Podkolzin A.S., Vedenie v teoriyu avtomatov, Nauka, M., 1985, 320 pp. | MR

[2] Budach L., “Automata and labyrinths”, Mathematische Nachrichten, 1978 | MR

[3] 16-ya letnyaya konferentsiya mezhdunarodnogo matematicheskogo Turnira gorodov http://www.turgor.ru/lktg/2004/avtom.ru/ru.ps

[4] Counter machine, http://en.wikipedia.org/wiki/Counter_machine

[5] Gray F., Pulse code communication, U.S. Patent 2,632,058, 1953

[6] Hilbert D., “Uber die stetige Abbildung einer Linie auf ein Flachenstuck”, Mathematische Annalen, 1891

[7] Peano G., “Sur une courbe, qui remplit toute une aire plane”, Mathematische Annalen, 1890

[8] Butz A.R., “Convergence with Hilbert's space-filling curve”, Journal of Computer and System Sciences, 1969 | MR