Carriers of algebra of algorithms

• Autorzy: Ovsyak V. , Ovsyak O.
• Języki publikacji: EN

Abstrakty

EN

Operations of modified system of algorithm algebras [10, 11] and algebra of algorithms [12-15] are presented in the paper. The paper shows operations of mathematical logic on the three-meaning alphabet. It considers converting of logical to operator values that are performed in the system of algorithmic algebras and its modifications. It presents constants, variables and operators, which are components of models of algorithms and systems, as predicates. It gives a comparative assessment of mono- and polycarrier algebras of algorithms.

Słowa kluczowe

EN

carrier of algebra; algebraic operations; system of algorithmic algebras; algebra of algorithms

• Wydawca: Wydawnictwo PAK
• Czasopismo: Measurement Automation Monitoring
• Rocznik: 2015
• Tom: Vol. 61, No. 4
• Strony: 98--100
• Opis fizyczny: Bibliogr. 15 poz., tab., wzory

Twórcy

autor

Ovsyak V.

• Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25 314, Kielce, Poland
• Ukrainian Academy of Printing, Pid Goloskom 19, 79 020, Lviv, Ukraine

autor

Ovsyak O.

• National University of Culture and Arts, Shuchevitcha 5, 79-020, Lviv, Ukraine

Bibliografia

• [1] Post L.: Finite Combinatory Processes - Formulation 1. Journal of Symbolic Logic. Vol. 1, No. 3, pp. 103-105.
• [2] Turing A. M.: On computable numbers, with an application to the Entscheidungsproblem . Proceedings of London Mathematical Society, Series 2. - Vol. 42, No. 3, 4, pp. 230-265.
• [3] Kolmogorov A. N.: On the concept of algorithm. Uspekhi Mat. Nauk 8:4, pp. 175-176 (in Russian); translated into English in Uspensky V.A., Semenov A.L.: Algorithms: Main Ideas and Applications, Kluwer, 1993.
• [4] Schönhage A.: Universelle Turing Speicherung. In J. Dörr and G. Hotz, Editors, Automatentheorie und Formale Sprachen, Bibliogr. Institut, Mannheim, 1970, pp. 369-383.
• [5] Aho A. V., Hopcroft J. E., Ullman J. D.: The design and analysis of computer algorithms. Addison-Wesley Publishing Company, 1974.
• [6] Church A.: An unsolvable problem of elementary number theory. American Journal of Mathematics. Vol. 58, pp. 345-363.
• [7] Kleene S. C.: Origins of recursive function theory. Annals of the History of Computing, 3:1 (January 1981), pp. 52-67.
• [8] Markov A. A.: Theory of algorithms. Editions of Academy of Sciences of the USSR. - Vol. 38, 1951. - pp. 176-189 (in Russian); translated into English in American Mathematical Society Transactions, 1960, series 2, 15, pp. 1-14.
• [9] Krinitski N. A.: Algorithms around us. Mir, Moscow, 1988 (in Russian); also translated to Spanish (Algoritmos a nuestro alrededor).
• [10] Gluschkow W. M., Zeitlin G. E., Justchenko E. L.: Algebra. Sprachen. Programmierung. Akademie-Verlag, Berlin 1980. – 340 p.
• [11] Zeitlin G. E. Algebraicheskaja algoritmika: teoria i primenienia. Kibernetika i systemny analiz. No 1, 2003, pp. 8 – 18 (Rus.).
• [12] Owsiak W., Owsiak A., Owsiak J.: Teoria algorytmów abstrakcyjnych i modelowanie matematyczne systemów informacyjnych. Wyd. Pol. Opolskiej, Opole, 2005.
• [13] Owsiak W., Owsiak A.: Rozszerzenie algebry algorytmów. Pomiary, Automatyka, Kontrola. No. 2, 2010, pp. 184-188.
• [14] Ovsyak O. V., Ovsyak V. K.: Modificirowannaja algebra algorytmov i instrumentalne sredstva obrabotki formul algebry algorytmov. Upravlajuszczije sistemy i masziny. No. 1, 2013, pp. 27–36 (Rus.).
• [15] Ovsyak O.: Comparison of algebraic methods for algorithm transform. Pomiary, Automatyka, Kontrola. No. 10, 2013, pp. 1046-1048.