Skip to main content
Log in

Functional completeness criteria in Dijkstra algebra

  • Cybernetics
  • Published:
Cybernetics and Systems Analysis 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.

References

  1. V. M. Glushkov, “Automata theory and formal transformations of microprograms,” Kibernetika, No. 5, 1–10 (1965).

    MATH  Google Scholar 

  2. U. Dahl, E. Dijkstra, and C. Hoare, Structured Programming [Russian translation], Mir, Moscow 3rd Edition, Naukova Dumka, Kiev (1989).

    Google Scholar 

  3. Yu. V. Kapitonova and A. A. Letichevskii, Mathematical Theory of Computer System Design [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  4. G. E. Tseitlin, “Problem of identical transformations of schemes of structured programs with closed logical conditions, parts 1–3,” Kibernetika, No. 3, 50–57 (1978), No. 4, 10–18 (1978), No. 5, 44–51 (1979).

    MATH  MathSciNet  Google Scholar 

  5. G. E. Tseitlin, “Formal transformation in three-valued logic of structured programming,” Proc. 12th Int. Symp. on Multiple-Valued Logic, Paris (1982), pp. 336–340.

  6. P. M. Ivanov, “Automaton expressions in a system of algorithmic algebras with a commutative algebra of conditions,” Kibernetika, No. 2, 16–20 (1978).

    MATH  Google Scholar 

  7. A. L. Semenov, “Some algorithmic problems for systems of algorithmic algebras,” Dokl. Akad. Nauk SSSR,239, No. 5, 1036–1066 (1978).

    Google Scholar 

  8. D. B. Bui and V. N. Red’ko, “Primitive program algebras of computable functions,” Kibernetika, No. 3, 68–74 (1987).

    MathSciNet  Google Scholar 

  9. D. B. Bui, B. V. Gubskii, and V. N. Red’ko, “Completeness problems in classes of computable named functions,” Kibernetika, No. 4, 58–65 (1988).

    MathSciNet  Google Scholar 

  10. D. B. Bui and I. V. Red’ko, “Completeness problems in classes of denotate-preserving computable functions,” Programmirovanie, No. 4, 56–68 (1991).

    Google Scholar 

  11. Yu. V. Golunkov, Completeness Problem in Functional Systems of Program Type [in Russian], doctoral dissertation, Kazan’ (1989).

  12. Yu. V. Golunkov, “On completeness of operations in systems of algorithmic algebras,” in: Algorithms and Automata [in Russian], Izd. Kazanskogo Univ., Kazan’ (1978), pp. 11–53.

    Google Scholar 

  13. E. L. Post, “The two-terminal iterative systems of mathematical logic,” Ann. Math. Stud., No. 5, 147 (1941).

    MathSciNet  Google Scholar 

  14. S. V. Yablonskii, G. P. Gavrilov, and B. V. Kudryavtsev, Functions of the Algebra of Logic and Post Classes [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  15. S. V. Yablonskii, Introduction to Discrete Mathematics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  16. A. I. Mal’tsev, “Iterative algebras and Post varieties,” Collected Works [in Russian], Vol. 2, pp. 316–330, Moscow (1976).

    Google Scholar 

  17. G. E. Tseitlin, “On infinitely generated subalgebras of the modified Post algebra,” Kibernetika, No. 2, 43–45 (1971).

    MATH  Google Scholar 

  18. V. G. Bondarchuk and G. E. Tseitlin, “On algebras of periodically defined transformations of an infinite register,” Kibernetika, No. 1, 18–28 (1969).

    Google Scholar 

  19. L. A. Kaluzhnin, “On algorithmization of mathematical problems,” Probl. Kibern., No. 2, 51–69 (1959).

    MATH  Google Scholar 

  20. G. E. Tseitlin and E. L. Yushchenko, “Algebra of algorithms and Kaluzhnin’s graph-schemes,” Kibern. Sist. Anal., No. 2, 3–17 (1994).

    MathSciNet  Google Scholar 

  21. Yu. I. Yanov, “On logical algorithm schemes,” Probl. Kibern., No. 1, 75–127 (1958).

    MATH  Google Scholar 

  22. A. P. Ershov, “On Yanov operator schemes,” Probl. Kibern., No. 20, 181–201 (1967).

    Google Scholar 

  23. G. E. Tseitlin, “Formal aspects of structured programming with go to,” Programmirovanie, No. 1, 3–16 (1984).

    MATH  MathSciNet  Google Scholar 

  24. G. E. Tseitlin, “Searching and sorting: classification, transformation, synthesis, I, II,” Avtomat. Telemekh., No. 4, 147–154, No. 5, 156–165 (1992).

    MATH  MathSciNet  Google Scholar 

  25. G. E. Tseitlin, “Symbolic processing strategies and synthesis of algorithms and programs,” Programmirovanie, No. 1, 29–43 (1993).

    MATH  Google Scholar 

  26. G. E. Tseitlin, “Design of symbolic processing algorithms,” Kibern. Sist. Anal., No. 2, 17–30 (1993).

    MATH  MathSciNet  Google Scholar 

  27. E. L. Yushchenko, G. E. Tseitlin, V. P. Gritsai, and T. K. Tersyan, Multilevel Structured Program Design: Theoretical Principles and Tools [in Russian], Finasy i Statistika, Moscow (1989).

    Google Scholar 

Download references

Authors

Additional information

The study was supported by the International Soros Program for basic Research and Education in Exact Sciences of the International Foundation “Renaissance,” grant No. VA0000.

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 28–40, September–October, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tseitlin, G.E. Functional completeness criteria in Dijkstra algebra. Cybern Syst Anal 31, 659–668 (1995). https://doi.org/10.1007/BF02366313

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02366313

Keywords

Navigation