Methods of Ordering in Computer Sciences and Information Technologies
Creators
- 1. Kyiv National University of Culture and Arts, Ukraine
Description
The purpose of the article is to analyze the known methods of ordering in computer science.
The research methodology consists of methods of ordered pairs, relations, Gödel numbering, and Glushkov’s system of algorithmic algebras.
The scientific novelty is to create a method of both description and transformation of orders.
Conclusions. In the methods of ordered pairs, relations, Gödel numbering, mathematical logic, Post and Turing machines, and the modified system of Glushkov’s algorithmic algebras there is no possibility of equivalent transformations of orders which are available in algorithms.
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References
- Aho, A.V., Hopcroft, J.E. and Ullman, J.D., 1974. The design and analysis of computer algorithms. Addison-Wesley Publishing Company.
- Church, A., 1936. An unsolvable problem of elementary number theory. American Journal of Mathematics, 58, pp.345-363.
- Gluschkow, W.M., Zeitlin, G.E. and Justchenko, J.L. 1980. Algebra. Sprachen. Programmierung. Berlin: Akademie-Verlag.
- Glushkov, V.M., Tceitlin, G.E. and Iushchenko, E.L., 1989. Algebra. Iazyki. Programmirovanie [Algebra. Languages. Programming]. Kyiv: Naukova dumka.
- Gödel numbering. Wikipedia. [online] Avialable at: <https://en.wikipedia.org/wiki/G%C3%B6del_numbering> [Accessed 15 April 2022].
- Kleene, S.C., 1981. Origins of recursive function theory. Annals of the History of Computing, 3 (1), pp.52-67.
- Kolmogorov, A.N., 1953. O poniatii algoritma [On the concept of an algorithm]. Uspekhi matematicheskikh nauk, 8 (4), pp.175-176.
- Krinitckii, N.A., 1988. Algoritmy vokrug nas [Algorithms around us]. Moscow: Mir.
- Kryvyi, S.L., 2014. Dyskretna matematyka [Discrete Mathematics]. Chernivtsi: Kyiv: Bukrek.
- Kuratovskii, K. and Mostovskii, A., 1970. Teoriia mnozhestv [Theory of sets]. Translation from English M.I. Kratko. Moscow: Mir.
- Markov, A.A., 1951. Teoriia algorifmov [Theory of algorithm]. In: Trudy Matematicheskogo instituta im. V.A. Steklova AN SSSR [Proceedings of the Mathematical Institute. V.A. Steklov Academy of Sciences of the USSR], 38, pp.176-189.
- Nikitchenko, M.S., 2010. Teoretychni osnovy prohramuvannia [Theoretical bases of programming]. Nizhyn: Vydavnytstvo NDU imeni Mykoly Hoholia.
- Ordered pair. Wikipedia. [online] Avialable at: <https://en.wikipedia.org/wiki/Ordered_pair> [Accessed 15 April 2022].
- Post, E.L., 1936. Finite Combinatory Processes Formulation 1. Journal of Symbolic Logic, 1, pp.103-105.
- Schönhage, A., 1970. Universelle Turing Speicherung. In: J. Dörr and G. Hotz eds. Automatentheorie und Formale Sprachen, Bibliogr. Institut, Mannheim, pp.369-383.
- Turing, A.M., 1937. On computable numbers, with an application to the Entscheidungs problem. Proceedings of London Mathematical Society, series 2, 42, pp.230-265.
- Vinogradov, I.M. ed., 1985. Matematicheskaia entciklopediia [Mathematical Encyclopedia]. Moscow: Sovetskaia entciklopediia.