Geodesic
The closure operator with the equality predicate branching on the set of partial Boolean functions
Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 80-88.

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On the set $P_2^*$ of partial Boolean functions, we consider the closure operator with the equality predicate branching. We prove that each closed class with respect to this operator is generated in $P_2^*$ by the set of all its functions depending on at most two variables. In the paper, all maximal and submaximal classes in $P_2^*$ and all closed classes generated by one one-place or two-place function are presented. This research was supported by the Russian Foundation for Basis Research, grant 06–01–00438. 
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S. S. Marchenkov. The closure operator with the equality predicate branching on the set of partial Boolean functions. Diskretnaya Matematika, Tome 20 (2008) no. 3, pp. 80-88. http://geodesic.mathdoc.fr/item/DM_2008_20_3_a7/

[1] Alekseev V. B., Voronenko A. A., “O nekotorykh zamknutykh klassakh v chastichnoi dvuznachnoi logike”, Diskretnaya matematika, 6:4 (1994), 58–79 | MR | Zbl

[2] Golunkov Yu. V., “Kriterii polnoty sistemy operatsii v operatornykh algoritmakh, realizuyuschikh funktsii $k$-znachnoi logiki”, Veroyatnostnye metody i kibernetika, 17 (1980), 23–34 | MR | Zbl

[3] Marchenkov S. S., Zamknutye klassy bulevykh funktsii, Fizmatlit, Moskva, 2000 | MR | Zbl

[4] Marchenkov S. S., “Operatory zamykaniya s razvetvleniem po predikatu”, Vestnik MGU. Ser. 1. Matem., mekh., 2003, no. 6, 37–39 | MR | Zbl

[5] Taimanov V. A., “O funktsionalnykh sistemakh $k$-znachnoi logiki s operatsiyami zamykaniya programmnogo tipa”, Dokl. AN SSSR, 268:6 (1983), 1307–1310 | MR | Zbl

[6] Freivald R. V., “Kriterii polnoty dlya chastichnykh funktsii algebry logiki i mnogoznachnykh logik”, Dokl. AN SSSR, 167:6 (1966), 1249–1250 | MR | Zbl

[7] Freivald R. V., “Funktsionalnaya polnota dlya ne vsyudu opredelennykh funktsii algebry logiki”, Diskretnyi analiz, 1966, no. 8, 55–68 | MR | Zbl

[8] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 1986 | MR | Zbl

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