Cybernetics

, Volume 17, Issue 2, pp 157–167 | Cite as

The algebras of partial functions and their invariants

  • B. A. Romov
Article

Keywords

Operating System Artificial Intelligence System Theory Partial Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    E. Post, “Introduction to a general theory of elementary propositions,” Am. J. Math.,43, 163–185 (1921).Google Scholar
  2. 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. 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. 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. 5.
    A. I. Mal'tsev, “Iterative algebras and Post manifolds,” Algebra Logika, Novosibirsk,5, No. 2, 5–14 (1966).Google Scholar
  6. 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. 7.
    A. Mansoux, “Théories de Galois locales,” Compt. Rend. Acad. Sci. Paris,282, No. 15, 759–762 (1976).Google Scholar
  8. 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. 9.
    B. A. Romov, “Galois correspondence between iterative Post algebras and relations on infinite sets,” Kibernetika, No. 3, 62–64 (1977).Google Scholar
  10. 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. 11.
    A. Fraenkel and Y. Bar-Hillel, Foundations of Set Theory [Russian translation], Mir, Moscow (1966).Google Scholar
  12. 12.
    G. P. Gavrilov, “On functional completeness in countably-valued logics,” Probl. Kibernet.,15, 5–64 (1965).Google Scholar
  13. 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. 14.
    I. Rosenberg, “Maximal clones on algebras A and Ar,” Rend. Sirc. Mat. Palermo,18, Ser. II, 329–333 (1969).Google Scholar
  15. 15.
    B. A. Romov, “On formulability of predicates on a finite model,” Kibernetika, No. 1, 41–42 (1971).Google Scholar
  16. 16.
    Yu. V. Golunkov, “Algorithmic completeness and complexity of microprograms,” Kibernetika, No. 3, 1–15 (1977).Google Scholar
  17. 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. 18.
    A. Foster, “Functional completeness in the small,” Math. Annal.,143, 29–58 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • B. A. Romov

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