Abstract
A classical theorem of Post [1] describes five precomplete classes in the set of Boolean functions. In [2], it was shown that there exist 18 precomplete classes of functions of three-valued logic. In [1, 2], the closure of sets of functions with respect to the substitution operator was studied. We consider two closure operators on functions of three-valued logic, which are obtained by supplementing the substitution operator by closures with respect to two identifications of function values, and prove the existence of three precomplete classes for one of these operators and five precomplete classes for the other.
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References
E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, in Ann. of Math. Stud. (Princeton Univ. Press, Princeton, NJ, 1941), Vol. 5.
S. V. Yablonskii, “Functional constructions in k-valued logic,” in Trudy Mat. Inst. Steklov, Vol. 51: Mathematical Logic and Its Applications to Some Questions of Cybernetics: Collection of Papers (Izd. Akad. Nauk SSSR, Moscow, 1958), pp. 5–142 [in Russian].
S. S. Marchenkov, S-Classification of Functions of Three-Valued Logic (Fizmatlit, Moscow, 2001) [in Russian].
J. Slupecki, “Kryterium petnosci wielowartoskiowych systemow logiki zdan,” C. R. Soc. Sci. Lett. Varsovie. Cl. III 32, 102–109 (1939).
S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and Post Classes (Nauka, Moscow, 1966) [in Russian].
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Esin, A.A. On function classes in P 3 precomplete with respect to a strengthened closure operator. Math Notes 83, 594–603 (2008). https://doi.org/10.1134/S0001434608050027
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DOI: https://doi.org/10.1134/S0001434608050027