Badmaev, Sergeĭ Aleksandrovich; Sharankhaev, Ivan Konstantinovich On maximal clones of partial ultrafunctions on a two-element set. (Russian. English summary) Zbl 1350.08002 Izv. Irkutsk. Gos. Univ., Ser. Mat. 16, 3-18 (2016). Summary: Class of discrete functions from a finite set \(A\) to set of all subsets of \(A\) is a natural generalization of the class of many-valued functions on \(A\) (\(k\)-valued logic functions). Functions of this type are called multifunctions or multioperations on \(A\), and are used, for example, in the solution of the functional equations, in logical and technical systems. It is obvious that the superposition in the usual sense not appropriate for multifunctions, therefore, we need to expand the standard concept of superposition. We note there are various ways to determine the operation of superposition of multifunctions, one of such methods is considered in this paper. Multifunctions on \(A\) with this superposition are called partial ultrafunctions on \(A\). In this article starting set \(A\) is two-element set and we consider classical problem of theory of discrete functions – description of clones – sets of functions closed with respect to the operation of superposition and containing all the projections. We got a description of the two maximal clones of partial ultrafunctions of a two-element set by the predicate approach. Cited in 7 Documents MSC: 08A40 Operations and polynomials in algebraic structures, primal algebras 03B50 Many-valued logic 06E30 Boolean functions Keywords:multifunction; partial ultrafunction; superposition; clone; maximal clone PDFBibTeX XMLCite \textit{S. A. Badmaev} and \textit{I. K. Sharankhaev}, Izv. Irkutsk. Gos. Univ., Ser. Mat. 16, 3--18 (2016; Zbl 1350.08002) Full Text: Link References: [1] Badmaev, S. A.; Sharankhaev, I. K., Minimal Partial Ultraclones on a Two-element Set (in Russian), Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika. [The Bulletin of Irkutsk State University], 3-9 (2014) · Zbl 1338.08001 [2] Badmaev, S. A., On Complete Sets of Partial Ultrafunctions on a Two-element Set (in Russian), Vestnik Buryat. Gos. Univ. Matem. , Inform., 3, 61-67 (2015) [3] Panteleyev, V. I., Completeness Criterion for Incompletely Defined Boolean Functions (in Russian), Vestnik Samar. Gos. Univ. Est. -Naush Ser., 68, 60-79 (2009) · Zbl 1319.03064 [4] Panteleyev, V. I., Completeness Criterion for Sub-defined Partial Boolean Functions (in Russian), Vestnik Novosibir. Gos. Univ. Ser.: Matem., Mechan., Inform., 3, 95-114 (2009) · Zbl 1249.06037 [5] Panteleyev, V. I., On Two Maximal Multiclones and Partial Ultraclones (in Russian), Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika. [The Bulletin of Irkutsk State University], 4, 46-53 (2012) · Zbl 1304.08003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.