Geodesic
On the directional movement of a collective of automata without a compass on a one-dimensional integer lattice
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 356-365

Voir la notice de l'article provenant de la source Math-Net.Ru

A collective of finite automata has to preserve unidirectional movement on one-dimensional integer lattice whose elements (vertices) are unlabelled. The automata does not distinguish between equally labelled vertices by their coordinates of direction (that means each automaton has no compass). We considered collectives consisting of an automaton and some pebbles, i.e. automata of the simplest form, whose positions are completely determined by automaton. We prove that a collective of automaton and a maximum of 2 pebbles cannot maintain movement direction on the one-dimensional integer lattice, but collective of automaton and 3 pebbles can. 
@article{ISU_2016_16_3_a13,
     author = {O. M. Kurganskyy and S. V. Sapunov},
     title = {On the directional movement of a collective of automata without a compass on a one-dimensional integer lattice},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {356--365},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a13/}
}
TY  - JOUR
AU  - O. M. Kurganskyy
AU  - S. V. Sapunov
TI  - On the directional movement of a collective of automata without a compass on a one-dimensional integer lattice
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2016
SP  - 356
EP  - 365
VL  - 16
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a13/
LA  - ru
ID  - ISU_2016_16_3_a13
ER  - 
%0 Journal Article
%A O. M. Kurganskyy
%A S. V. Sapunov
%T On the directional movement of a collective of automata without a compass on a one-dimensional integer lattice
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2016
%P 356-365
%V 16
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a13/
%G ru
%F ISU_2016_16_3_a13
O. M. Kurganskyy; S. V. Sapunov. On the directional movement of a collective of automata without a compass on a one-dimensional integer lattice. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 356-365. http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a13/