Abstract
We consider the functional system of vector functions of many-valued logic with the naturally defined operation of superposition and construct examples of closed classes of special type without a basis and with a countable basis.
Originally published in Diskretnaya Matematika (2016) 28, №2, 127–132 (in Russian)
References
[1] Yablonsky S.V., Introduction to Discrete Mathematics, Mir Publishers, Moscow, 2003 (in Russian), 384 pp.Suche in Google Scholar
[2] Malcev I., “Graduated products of Post algebras”, Note on multiple-valued logic, 18:13 (1995), 1–4.Suche in Google Scholar
[3] Malcev I., “Coordinated products of iterative algebras”, Proc. VIII Int. Conf. on Logic and Computer Science, Novi Sad, Yugoslavia, 1997, 1–2.Suche 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.1992.2.6.587Suche 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.1993.3.2.147Suche in Google Scholar
[6] Marchenkov S.S., “On precomplete classes in Cartesian products of P2 and P3”, Discrete Math. Appl., 4:3 (1994), 209–228.10.1515/dma.1994.4.3.209Suche in Google Scholar
[7] Romov B.A., “The algorithm for solving the completeness problem in the class of vector functional systems”, Matem. modeli slozhnykh sistem, IK AN USSR, Kiev, 1973, 151–155 (in Russian).Suche in Google Scholar
[8] Romov B.A., “On the lattice of subalgebras of Post algebras direct products of finite degree”, Matem. modeli slozhnykh sistem, IK AN USSR, Kiev, 1973, 156–168 (in Russian).Suche in Google Scholar
[9] Romov B.A., “Completeness on the square of the algebra logic functions and in the systems PktimesPl, Kibernetika, 4 (1987), 9–14 (in Russian).Suche in Google Scholar
[10] Romov B.A., “A series of maximum subalgebras of direct products of algebras of finite-valued logics”, Cybernetics and Systems Analysis, 25:3, 300–306.10.1007/BF01069983Suche in Google Scholar
[11] Romov B.A., “Functional completeness in P2 × Pk”, Cybernetics and Systems Analysis, 27:1, 1–10.10.1007/BF01068640Suche in Google Scholar
[12] Romov B.A., “The completness problem on the product of algebras of finite-valued logic”, Int. Symp. Multiple-Valued Logic, Boston, USA, 1994, 184–186.Suche 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_96Suche in Google Scholar
[14] Taymanov V.A., “On bases of closed classes in Pk × Pm”, Tez. dokl. VIII Vsesoyuzn. konf. “Problemy teoreticheskoy kibernetiki”, Irkutsk, 1985, 188–189 (in Russian).Suche in Google Scholar
[15] Yanov Yu.I., Muchnik A.A., “On the existence of k-valued closed classes without a finite basis”, Dokl. AN SSSR, 127:1 (1959), 44–46 (in Russian).Suche in Google Scholar
[16] Yablonskiy S.V., Gavrilov G.P., Kudryavtsev V.B., Logic algebra functions and Post classes, Nauka, Moscow, 1966 (in Russian), 120 pp.Suche in Google Scholar
[17] Post E.L., “Introduction to a general theory of elementary propositions”, Amer. J. Math., 43 (1921), 163–185.10.2307/2370324Suche in Google Scholar
[18] Post E.L., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941, 122 pp.10.1515/9781400882366Suche in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Extension of the Rissanen algorithm to the factorization of block-Hankel matrices for solving systems of linear equations
- On asymptotics of branching processes with immigration
- On some measures of complexity of finite Abelian groups
- Complexity classification of the edge coloring problem for a family of graph classes
- On FE-precomplete classes in countable-valued logic
- On 1-stable perfectly balanced Boolean functions
- On bases of closed classes of vector functions of many-valued logic
- On the asymptotic normality of some sums of dependent random variables
- On serial rings
Artikel in diesem Heft
- Frontmatter
- Extension of the Rissanen algorithm to the factorization of block-Hankel matrices for solving systems of linear equations
- On asymptotics of branching processes with immigration
- On some measures of complexity of finite Abelian groups
- Complexity classification of the edge coloring problem for a family of graph classes
- On FE-precomplete classes in countable-valued logic
- On 1-stable perfectly balanced Boolean functions
- On bases of closed classes of vector functions of many-valued logic
- On the asymptotic normality of some sums of dependent random variables
- On serial rings