Geodesic
On completeness of multifunction set of rank 2
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 465-471 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of completeness of the set of functions from a finite set $A$ to set of all subsets of $A$ is studied. Functions of this kind are called multifunctions on $A$, they generalize the well-known class of functions of $k$-valued logic. The usual superposition adopted for functions of $k$-valued logic is not suitable for multifunctions. In the paper one of the types of superpositions that are commonly used for multifunctions is considered. We prove necessary and sufficient condition for the completeness of an arbitrary set of multifunctions on $\{0, 1\}$ which contains all unary Boolean functions with respect to given superposition.
Keywords: Boolean function, multifunction, rank, completeness set.
Mots-clés : superposition 
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Sergey A. Badmaev; Ivan K. Sharankhaev. On completeness of multifunction set of rank 2. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 465-471. http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a7/

[1] V.V. Tarasov, “Completeness criterion for partial logic functions”, Problemy kibernetiki, 30 (1975), 319–325 (in Russian) | Zbl

[2] R.V. Freivald, “Completeness criterion for partial functions of algebra logic and many-valued logics”, Doklady AN SSSR, 167 (1966), 1249–1250 (in Russian) | MR

[3] S.A. Badmaev, I.K. Sharankhaev, “Minimal partial ultraclones on a two-element set”, Izvestiya Irk. Gos. Univ. Ser. Matematika, 9 (2014), 3–9 (in Russian) | MR | Zbl

[4] V.I. Panteleyev, “On Two maximal multiclones and partial ultraclones”, Izvestiya Irk. Gos. Univ. Ser. Matematika, 5:4 (2012), 46–53 (in Russian)

[5] S.A. Badmaev, I.K. Sharankhaev, “On some completeness criterion of multifunction set”, International Conference Maltsev meeting (Novosibirsk, 2017), 139 (in Russian)

[6] V.I. Panteleyev, “Special representations of sub-defined partial Boolean functions”, Uchenie Zapiski Kazan. Gos. Univ. Ser. Fiziko-Matem. Nauki, 151:2 (2009), 114–119 (in Russian)

[7] S.A. Badmaev, “On some maximal clone of partial ultrafunctions on a two-element set”, Journal of SFU. Math. and Phys., 10:2 (2017), 140–145 | MR