On the automaton determinization of sets of superworks
Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 84-97
We introduce the concept of a determinising automaton which, for every superword taken from a given set fed into its input, beginning with some step, at any time $t$ yields the value of the input word at time $t+1$, that is, predicts the input superword. We find a criterion whether a given set of superwords is determinisable, that is, whether for the set there exists a determinising automaton. We give the best (in some sense) method to design a determinising automaton for an arbitrary determinisable set of superwords. For some determinisable sets we present optimal and asymptotically optimal determinising automata.
@article{DM_2006_18_2_a5,
author = {A. G. Verenkin and \`E. \`E. Gasanov},
title = {On the automaton determinization of sets of superworks},
journal = {Diskretnaya Matematika},
pages = {84--97},
year = {2006},
volume = {18},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2006_18_2_a5/}
}
A. G. Verenkin; È. È. Gasanov. On the automaton determinization of sets of superworks. Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 84-97. http://geodesic.mathdoc.fr/item/DM_2006_18_2_a5/
[1] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Vvedenie v teoriyu avtomatov, Nauka, Moskva, 1985 | MR
[2] Trakhtenbrot B. A., Barzdin Ya. M., Konechnye avtomaty (povedenie i sintez), Nauka, Moskva, 1970 | MR
[3] Vinogradov I. M., Vvedenie v teoriyu chisel, Nauka, Moskva, 1981
[4] Kostrikin A. I., Osnovnye struktury algebry, Fizmatlit, Moskva, 2000