Skip to main content
Log in

The algebras of partial functions and their invariants

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. E. Post, “Introduction to a general theory of elementary propositions,” Am. J. Math.,43, 163–185 (1921).

    Google Scholar 

  2. R. V. Freivald, “Completeness criteria for partial functions of the algebra of logic and many-valued logics,” Dokl. Akad. Nauk SSSR,167, No. 6, 1249–1250 (1966).

    Google Scholar 

  3. R. V. Freivald, “Functional completeness for not everywhere defined functions of the algebra of logic,” Diskretn. Anal., Novosibirsk, No. 8, 55–68 (1966).

    Google Scholar 

  4. B. A. Romov, “Algorithmic topics of synthesis in functional systems,” in: Development and Penetration of MIS and Automation, Izd. Inst. Avtomat., Kiev (1977), pp. 3–19.

    Google Scholar 

  5. A. I. Mal'tsev, “Iterative algebras and Post manifolds,” Algebra Logika, Novosibirsk,5, No. 2, 5–14 (1966).

    Google Scholar 

  6. V. G. Bondarchuk, L. A. Kaluzhnin, V. N. Kotov, and B. A. Romov, “Galois theory for Post algebras. I, II,” Kibernetika, No. 3, 1–10; No. 5, 1–9, (1969).

    Google Scholar 

  7. A. Mansoux, “Théories de Galois locales,” Compt. Rend. Acad. Sci. Paris,282, No. 15, 759–762 (1976).

    Google Scholar 

  8. I. Rosenberg, “Une correspondence de Galois entre les algébres universelles et les relations dans le méme univers,” Compt. Rend. Acad. Sci. Paris,280, No. 10, 615–616 (1975).

    Google Scholar 

  9. B. A. Romov, “Galois correspondence between iterative Post algebras and relations on infinite sets,” Kibernetika, No. 3, 62–64 (1977).

    Google Scholar 

  10. I. Rosenberg, “Über die funktionale vollständigkeit in den mehrwertigen Logiken,” Rozpravy Ceskoslovenské Akademie Véd., Praha,80, No. 4, 1–93 (1970).

    Google Scholar 

  11. A. Fraenkel and Y. Bar-Hillel, Foundations of Set Theory [Russian translation], Mir, Moscow (1966).

    Google Scholar 

  12. G. P. Gavrilov, “On functional completeness in countably-valued logics,” Probl. Kibernet.,15, 5–64 (1965).

    Google Scholar 

  13. I. Rosenberg, “The set of maximal closed classes of operations on an infinite set A has a cardinality 2 exp 2 exp |A|,” Arch. Math. (Basel),27, No. 6, 561–568 (1976).

    Google Scholar 

  14. I. Rosenberg, “Maximal clones on algebras A and Ar,” Rend. Sirc. Mat. Palermo,18, Ser. II, 329–333 (1969).

    Google Scholar 

  15. B. A. Romov, “On formulability of predicates on a finite model,” Kibernetika, No. 1, 41–42 (1971).

    Google Scholar 

  16. Yu. V. Golunkov, “Algorithmic completeness and complexity of microprograms,” Kibernetika, No. 3, 1–15 (1977).

    Google Scholar 

  17. G. P. Gavrilov, “Precomplete classes of partial countably-valued logic containing all the functions of one variable,” Diskret. Anal., Novosibirsk, No. 28, 12–24 (1976).

    Google Scholar 

  18. A. Foster, “Functional completeness in the small,” Math. Annal.,143, 29–58 (1961).

    Google Scholar 

Download references

Authors

Additional information

Translated from Kibernetika, No. 2, pp. 1–11, March–April, 1981.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romov, B.A. The algebras of partial functions and their invariants. Cybern Syst Anal 17, 157–167 (1981). https://doi.org/10.1007/BF01069627

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01069627

Keywords

Navigation