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On some properties of vector functions of Boolean algebra

  • Vladimir A. Taimanov EMAIL logo
Published/Copyright: April 12, 2019

Abstract

The functional system of Boolean vector functions with naturally defined superposition operation is studied. Sufficient conditions for membership of a number of important vector functions in closed classes are given.


Note: Originally published in Diskretnaya Matematika (2018) 30, №1, 114–128 (in Russian).


References

[1] Yablonsky S.V., Introduction to Discrete Mathematics, Nauka, Moscow, 2003 (in Russian), 484 pp.Search in Google Scholar

[2] Malcev I., “Graduated products of Post algebras”, Note on multiple-valued logic, 18:13 (1995), 1–4.Search in Google Scholar

[3] Malcev I., “Coordinated products of iterative algebras”, Proc. VIII Int. Conf. on Logic Comput. Sci., Novi Sad, Yugoslavia, 1997, 1–2.Search in Google Scholar

[4] Marchenkov S. S., “On the completeness in the System P3 × P3”, Discrete Math. Appl., 2:6 (1992), 587–606.10.1515/dma.1992.2.6.587Search in Google Scholar

[5] Marchenkov S. S., “On the Slupecki classes in the systems Pk × … × Pl”, Discrete Math. Appl., 3:2 (1993), 147–160.10.1515/dma.1993.3.2.147Search in Google Scholar

[6] Marchenkov S. S., “Precomplete classes in the Cartesian products of P2 and P2”, Discrete Math. Appl., 4:4 (1994), 209–228.10.1515/dma.1994.4.3.209Search in Google Scholar

[7] Romov B.A., “Algorithm for solution of the completeness problem in a class of vector functional systems”, Mathematical models of complex systems, IK AN USSR, Kiev, 1973, 151–155 (in Russian).Search in Google Scholar

[8] Romov B.A., “On the lattice of finite degree subalgebras of Post algebras direct products”, Mathematical models of complex systems, IK AN USSR, Kiev, 1973, 156–168 (in Russian).Search in Google Scholar

[9] Romov B.A., “On the completeness on the square of the algebra logic functions and in the systems Pk × Pl”, Kibernetika, 4 (1987), 9–14 (in Russian).Search in Google Scholar

[10] Romov B.A., “On a series of direct product maximal subalgebras of finite-valued logics algebras”, Kibernetika, 3 (1989), 11–16 (in Russian).Search in Google Scholar

[11] Romov B.A., “On functional completeness in the system P2 × Pk”, Kibernetika, 1 (1991), 1–8 (in Russian).10.1007/BF01068640Search in Google Scholar

[12] Romov B.A., “The completness problem on the product of algebras of finite-valued logic”, ISMVL, Boston, USA, 1994, 184–186.Search in Google Scholar

[13] Taymanov V.A., “On cartesian powers of P2”, Dokl. Akad. Nauk SSSR, 270:6 (1983), 1327–1330 (in Russian).10.1007/3-540-18740-5_96Search in Google Scholar

[14] Taymanov V.A., “On bases of closed classes in Pk × Pm”, Tezisy dokladov VIII Vsesoyuznoy konferentsii “Problemy teoreticheskoy kibernetiki”, Irkutsk, 1985, 188–189 (in Russian).Search in Google Scholar

[15] Taimanov V.A., “On bases of closed classes of vector functions of multivalued logic”, Discrete Math. Appl., 27:2 (2017), 117–121.10.1515/dma-2017-0014Search in Google Scholar

[16] Yablonskiy S.In., Gavrilov G.P., Kudryavtsev In.B., Logic algebra functions and Post classes, Nauka, Moscow, 1966 (in Russian), 120 pp.Search in Google Scholar

[17] Post E.L., “Introduction to a general theory of elementary propositions”, Amer. J. Math., 43 (1921), 163–185.10.2307/2370324Search in Google Scholar

[18] Post E.L., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941, 122 pp.10.1515/9781400882366Search in Google Scholar

Received: 2017-04-18
Revised: 2017-12-28
Published Online: 2019-04-12
Published in Print: 2019-04-24

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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