Inductive representations of Boolean functions and the finite generation of the Post classes. (English. Russian original) Zbl 0555.03028
Algebra Logic 23, 1-19 (1984); translation from Algebra Logika 23, No. 1, 3-26 (1984).
The author studies some representations of Boolean functions and use them for establishing a series of interesting properties of functions from various Post classes, and in the proof of the existence of finite bases in all Post classes.
Reviewer: V.V.Gorlov
MSC:
| 03G20 | Logical aspects of Łukasiewicz and Post algebras |
| 06D25 | Post algebras (lattice-theoretic aspects) |
Keywords:
closed classes; Post algebras; representations of Boolean functions; Post classes; finite basesReferences:
| [1] | S. V. Yablonskii, ”Functional constructions in aK-valued logic,” Tr. Mat. Inst. Akad. Nauk SSSR,51, 5–142 (1958). |
| [2] | S. V. Yablonskii, Introduction to Discrete Mathematics [in Russian], Nauka, Moscow (1979). |
| [3] | S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and the Post Classes [in Russian], Nauka, Moscow (1966). |
| [4] | G. P. Gavrilov and A. A. Sapozhenko, Problem Book in Discrete Mathematics [in Russian], Nauka, Moscow (1977). · Zbl 0452.00010 |
| [5] | E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Princeton Univ. Press (1941). · Zbl 0063.06326 |
| [6] | E. L. Post, ”Introduction to a general theory of elementary propositions,” Am. J. Math.,43, No. 3, 163–185 (1921). · JFM 48.1122.01 · doi:10.2307/2370324 |
| [7] | S. V. Yablonskii, ”On certain results in the theory of functional systems,” in: Proc. Int. Congr. Math. (Helsinki, 1978), Vol. 2, Acad. Sci. Fennica, Helsinki (1980), pp. 963–971. |
| [8] | S. V. Yablonskii, ”On closed classes inP 2,” Probl. Kibern.,39, 262 (1982). |
| [9] | C. Benzaken, Treillis des familles de fonctions booléennes croissantes. Applications au coloriage d’un graphe, Séminaire Dubreil-Pisot (Algèbre et Théorie des Nombres), 19e année, No. 2, 1–13 (1965/66). |
| [10] | G. A. Shestopal, ”Simple bases in all closed classes of the algebra of logic,” Uch. Zap. Mosk. Gos Pedagog. Inst., No. 375, 156–178 (1971). |
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