Geodesic
Boolean reducibility
Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 40-53 
S. S. Marchenkov. Boolean reducibility. Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 40-53. http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/
@article{DM_2003_15_3_a1,
     author = {S. S. Marchenkov},
     title = {Boolean reducibility},
     journal = {Diskretnaya Matematika},
     pages = {40--53},
     year = {2003},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - Boolean reducibility
JO  - Diskretnaya Matematika
PY  - 2003
SP  - 40
EP  - 53
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/
LA  - ru
ID  - DM_2003_15_3_a1
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T Boolean reducibility
%J Diskretnaya Matematika
%D 2003
%P 40-53
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/
%G ru
%F DM_2003_15_3_a1

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

We define the operator of Boolean reducibility on the set of all infinite binary sequences. This operator is a variant of the operator of finite-automaton transformability when automata with several inputs and one state are considered. Each set $Q$ of Boolean functions containing a selector function and closed with respect to the operation of superposition of a special form defines the $Q$-reducibility and $Q$-degrees, that is, the sets of $Q$-equivalent sequences. We study properties of the partially ordered set $\mathcal L_Q$ of all $Q$-degrees, namely, the existence of maximal, minimal and the greatest elements, infinite chains and antichains, and upper bounds. The research was supported by the Russian Foundation for Basic Research, grant 03–01–00783.

[1] Rodzhers Kh., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, Moskva, 1972 | MR

[2] Reina G., “Stepeni avtomatnykh preobrazovanii”, Kibern. sb., 14 (1977), 95–106

[3] Gordon H. G., “Complete degrees of finite-state tranformability”, Information and Control, 32 (1976), 169–187 | DOI | MR | Zbl

[4] Bairasheva V. R., “Strukturnye svoistva avtomatnykh preobrazovanii”, Izvestiya vuzov. Matematika, 7 (1988), 34–39 | MR

[5] Marchenkov S. S., “Konechnye nachalnye segmenty verkhnei polureshetki konechno-avtomatnykh stepenei”, Diskretnaya matematika, 1:3 (1989), 96–103 | MR | Zbl

[6] Solovev V. D., “Struktura raspredeleniya informatsii v beskonechnoi posledovatelnosti”, Diskretnaya matematika, 8:2 (1996), 97–107 | MR