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A problem of completeness of S-sets of deterministic functions. (English. Russian original) Zbl 1304.68096
Mosc. Univ. Math. Bull. 63, No. 5, 211-213 (2008); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 5, 57-59 (2008).
Summary: A problem of completeness of S-deterministic functions determined on words of length $$\tau$$ is considered. The set of all precomplete classes forming the minimal criterial system for recognition of the completeness of arbitrary S-sets of deterministic functions is described in terms of preservation of relations (predicates).
##### MSC:
 68Q45 Formal languages and automata 08A40 Operations and polynomials in algebraic structures, primal algebras
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##### References:
 [1] V. B. Kudryavtsev, S. V. Aleshin, and A. S. Podkolzin, Introduction to the Theory of Automata (Nauka, Moscow, 1985) [in Russian]. [2] Y. Rosenberg, La structure des fonctions de plusieure variables sur un ensemble fini, C.r. Acad. sci. Paris, 3817 (1965). · Zbl 0144.01002 [3] V. B. Kudryavtsev, ”Properties of S-Systems of Functions in k-Valued Logic,” Elektronische Informationsverarbeitung und Kybernetik. 9(1–2), 8 (1973). [4] V. A. Buevich and M. A. Podkolzina, ”Completeness Criterion of S-Completeness of Sets of Deterministic Functions,” in Matem. Voprosy Kibern. 16 (Nauka, Fizmatlit, Moscow, 2008), pp. 191–239. · Zbl 1202.03033 [5] V. A. Buevich, ”$$\tau$$-Completeness in the Class of Deterministic Functions,” Dokl. Russ. Akad. Nauk 326(3), 399 (1992). · Zbl 0921.03026
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