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Algebraic Algorithmics: Theory and Applications

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Cybernetics and Systems Analysis Aims and scope

Abstract

This article is a review of works on the algebra of algorithms, which is a new promising line of investigation in the field of algebraic algorithmics and is progressing rapidly in Ukraine and abroad. To this line belong explorations into a multilevel structural software design method developed at the Automatic Programming Department at the V. M. Glushkov Cybernetics Institute of the Academy of Sciences of Ukraine.

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REFERENCES

  1. P. Naudin and C. Quitti, Algebraic Algorithmics [Russian translation], Mir, Moscow (1999).

    Google Scholar 

  2. V. M. Glushkov, “Theory of automata and formal transformations of microprograms,” Kibernetika, No.5, 1-10 (1965).

  3. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, Algebra, Languages, and Programming [in Russian], 3rd ed., Naukova Dumka, Kiev (1989) ([German translation]: Akadem. Verlag, Berlin (1980)).

    Google Scholar 

  4. V. M. Glushkov, Yu. V. Kapitonova, and A. A. Letichevskii, Computer-Aided Design of Computers [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  5. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, “Theory of language processors and parallel computations,” Kibernetika, No. 1, 1-19 (1979).

  6. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, Methods of Symbolic Multiprocessing [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  7. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, “Multilevel structured program design: Formalization and applications,” Kibernetika, No. 4, 42-65 (1981).

  8. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, “The theory of language processors and homogeneous structures,” in: 2nd Intern. Symp. on Programming (Paris) (1976), pp. 201-218.

  9. V. M. Glushkov, G. E. Tseitlin, and E. L. Yushchenko, “Certain problems of the theory of structured program schemes,” Inform. Proc. Lect., 7, No. 6, 253-260 (1978).

    Google Scholar 

  10. V. N. Red'ko, “Compositions of programs and composition programming,” Programmirovanie, No. 5, 3-24 (1978).

  11. V. N. Red'ko, “Foundations of programmology: An explicative basis,” Vestn. Intern. Solomon Univ., No. 1, 13-42 (2000).

  12. V. N. Red'ko and E. L. Yushchenko, “Algorithmic languages and translating systems,” Kibernetika, No. 5, 87-91 (1967).

  13. I. V. Vel'bitskii and E. L. Yushchenko, “A metalanguage oriented towards syntactic analysis and control,” Kibernetika, No. 2, 50-54 (1970).

  14. E. L. Yushchenko and E. M. Lavrishcheva, “A method of analysis of programs on the basis of SM-grammars,” Kibernetika, No. 2, 41-45 (1972).

  15. O. L. Perevozchikova and E. L. Yushchenko, Dialogue Systems [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  16. L. P. Babenko and K. M. Lavrishcheva, Foundations of Program Engineering: An Educational Book [in Ukrainian], Tov. “Znannya” (Higher Education of the XXIth century), KOO, Kyiv (2001).

    Google Scholar 

  17. I. V. Sergienko, V. V. Skopetskii, and V. S. Deineka, “Some questions of computer-aided investigation of complex physical fields,” in: Application Packages: Operational Experience, Nauka, Moscow (1989), pp. 45-54.

    Google Scholar 

  18. A. N. Kolmogorov and V. A. Uspenskii, “An approach to the definition of an algorithm,” UMN, 13, No.4 (82), 3-28 (1958).

    Google Scholar 

  19. G. E. Tseitlin, “Structured programming in symbolic multiprocessing,” Kibernetika, No. 5, 22-30 (1983).

  20. G. E. Tseitlin, “Formal aspects of structural programming with GO TO,” Programmirovanie, No. 1, 3-16 (1984).

  21. G. E. Tseitlin, “Identity transformations for structured-program schemes with closed logic conditions. I, II, III,” Kibernetika, No. 3, 50-57 (1978), No. 4, 10-18, No. 5, 44-51 (1979).

  22. A. A. Letichevskii, “On acceleration of iterations of monotone operators,” Kibernetika, No. 4, 1-7 (1976).

  23. E. L. Yushchenko, “Identity transformations of nondeterministic program schemes in systems of algorithmic algebras,” Kibernetika, No. 3, 58-64 (1982).

  24. V. P. Panfil'yenko, “Deadlocks in parallel regular program schemes,” in: Izd. IK NANU, Kiev (1986), pp. 80-82.

  25. G. E. Tseitlin and A. V. Bakulin, “Multilevel structured program designs and correctness proving,” Kibernetika, No. 5, 98-107 (1991).

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

  27. G. E. Tseitlin and E. L. Yushchenko, “Algebra of algorithms and Kaluzhnin's graph-schemas,” Kibern. Sist. Anal., No. 2. p. 3-17 (1994).

  28. G. E. Tseitlin, An Introduction to Algorithmics [in Russian], Sfera, Kiev (1998).

    Google Scholar 

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

    Google Scholar 

  30. E. L. Yushchenko, S. V. Surzhko, G. E. Tseitlin, and A. I. Shevchenko, Algorithmic Algebras [in Ukrainian], IZMN, Kyiv (1997).

    Google Scholar 

  31. E. L. Yushchenko, Address Programming [in Russian], Gostekhizdat Ukr. SSR, Kiev (1963).

    Google Scholar 

  32. G. M. Kirsanov, G. E. Tseitlin, and E. L. Yushchenko, “Application of microprogram algebras to some questions of automatic programming,” in: Mat. Obesp. ETsVM, IK AN Ukr. SSR, Kiev (1971), pp. 99-117.

    Google Scholar 

  33. G. M. Kirsanov, G. E. Tseitlin, and E. L. Yushchenko, “ANALITIK: A program package for proving identities (theorems) in axiomatic algorithmic-algebra system,” Kibernetika, No. 4, 28-33 (1979).

  34. A. N. Petrushenko, “Algebras of dialogue algorithms and hyperschemes: Some their properties and applications,” Vestn. Intern. Solomon Univ., No. 4, 110-123 (2000).

  35. G. E. Tseitlin, “Algorithmic algebras of data structures and multilevel program design,” Programmirovanie, No. 3, 8-16 (1986).

  36. G. E. Tseitlin and E. L. Yushchenko, “Representation of languages in Bobsled (BS) automata,” Kibernetika, No. 6, 40-52 (1974).

  37. S. A. Zhukov, “Time complexity in the operation of a two-way parser,” Kibernetika, No. 4, 105-111 (1979).

  38. E. L. Yushchenko, Yu. L. Ivas'kiv, and G. E. Tseitlin, “Multilevel block design of discrete devices using algorithmic algebras,” Kibern. Sist. Anal., No. 2, 42-52 (1995).

  39. L. I. Nagornaya, G. E. Tseitlin, and E. L. Yushchenko, “Multilayer syntactic analysis of parallel programming systems,” Kibernetika, No. 1, 90-97 (1979).

  40. E. L. Yushchenko, G. E. Tseitlin, V. P. Gritsai, and T. K. Terzyan, Multilevel Structured Program Design: Theoretical Foundations and Tools [in Russian], Finansy i Statistika (1989).

  41. G. E. Tseitlin, “Systems of algorithmic algebras and automatic programming,” Probl. Progr., No. 1–2, 15-25 (2002).

  42. G. E. Tseitlin and E. L. Yushchenko, “Formalized program specifications and transformation synthesis,” Kibern. Sist. Anal., No. 1, 127-152 (1993).

  43. P. Cohn, Universal Algebra [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  44. G. E. Tseitlin, Algebra of Logic and Program Design [in Ukrainian], Naukova Dumka, Kyiv (1994).

    Google Scholar 

  45. G. E. Tseitlin, “The problem of functional completeness of metaalgebras of regular events,” Kibern. Sist. Anal., No. 6, 14-27 (2000).

  46. G. E. Tseitlin, “Functional completeness in iterative metaalgebras,” Kibern. Sist. Anal., No. 2, 28-45 (1998).

  47. G. Booch, Object-Oriented Analysis and Design with Applications, Addison-Wesley, Santa Clara, California (1993).

    Google Scholar 

  48. G. E. Tseitlin and G. V. Yusim, “Algebraic foundations of algorithmics and promising information technologies,” Probl. Upr. Inf., No. 6, 89-95 (1997).

  49. S. D. Pogorelyi, T. K. Terzyan, G. S. Finin, and G. E. Tseitlin, “Knowledge integration in training programmer-engineers,” Vestn. Intern. Solomon Univ., No. 4, 5-12 (2000).

  50. L. I. Nagornaya, T. K. Terzyan, G. E. Tseitlin, and E. L. Yushchenko, “ORIENTIR: Audio tools for text construction,” Kibern. Sist. Anal., No. 2, 148-155 (1993).

  51. I. V. Sergienko, Informatics in Ukraine: Formation, Development, and Problems [in Ukrainian], Naukova Dumka, Kyiv (1999).

    Google Scholar 

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Tseitlin, G.E. Algebraic Algorithmics: Theory and Applications. Cybernetics and Systems Analysis 39, 6–15 (2003). https://doi.org/10.1023/A:1023860707232

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