Geodesic
On the classification of Post automaton bases by the decidability of the $A$-completeness property for definite automata
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 80-95 
D. N. Zhuk. On the classification of Post automaton bases by the decidability of the $A$-completeness property for definite automata. Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 80-95. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a6/
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     title = {On the classification of {Post} automaton bases by the decidability of the $A$-completeness property for definite automata},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider systems of the form $M=F\cup\nu$, where $F$ is some Post class and $\nu$ is a finite system of definite automata. We divide the Post classes into those for which the problem of $A$-completeness of such systems of definite automata is algorithmically decidable and those for which the problem of $A$-completeness is algorithmically undecidable.

[1] Post E., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941 | MR | Zbl

[2] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966 | MR

[3] Kratko M. I., “Algoritmicheskaya nerazreshimost problemy raspoznavaniya polnoty dlya konechnykh avtomatov”, Doklady AN SSSR, 155 (1964), 35–37 | MR | Zbl

[4] Buevich V. A., “Ob algoritmicheskoi nerazreshimosti raspoznavaniya $A$-polnoty dlya o.d.-funktsii”, Matematicheskie zametki, 12:6 (1972), 687–697

[5] Babin D. N., “Razreshimyi sluchai zadachi o polnote avtomatnykh funktsii”, Diskretnaya matematika, 4:4 (1992), 41–55 | MR | Zbl

[6] Buevich V. A., Usloviya $A$-polnoty dlya avtomatov, Izd-vo MGU, Moskva, 1986

[7] Babin D. N., “O klassifikatsii avtomatnykh bazisov Posta po razreshimosti svoistv polnoty i $A$-polnoty”, Doklady RAN, 367:4 (1999), 439–441 | MR | Zbl

[8] Buevich V. A., Klindukhova T. E., “Ob algoritmicheskoi nerazreshimosti zadach ob $A$-polnote i polnote dlya definitnykh ogranichenno-determinirovannykh funktsii”, Matem. voprosy kibernetiki, 10, 2001

[9] Zhuk D. N., Prismotrov Yu. N., “O probleme polnoty v klasse avtomatov bez obratnoi svyazi”, Intellektualnye sistemy, 11 (2007), 439–472

[10] Zhuk D. N., “O nerazreshimosti problemy polnoty dlya definitnykh avtomatov”, Intellektualnye sistemy, 12 (2008), 211–228

[11] Zhuk D. N., “Razreshimye sluchai zadachi ob $A$-polnote dlya definitnykh avtomatov”, Intellektualnye sistemy, 13 (2009), 273–312

[12] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Vvedenie v teoriyu avtomatov, Nauka, Moskva, 1985 | MR | Zbl

[13] Maltsev A. I., Algoritmy i rekursivnye funktsii, Nauka, Moskva, 1986 | MR