https://oldena.lpnu.ua/handle/ntb/42834
Title: | Комбінаторний метод мінімізації булевих функцій |
Other Titles: | Combinatorial method of minimizing boolean functions |
Authors: | Різник, В. В. Соломко, М. Т. Riznyk, V. V. Solomko, M. T. |
Affiliation: | Національний університет “Львівська політехніка” Lviv Polytechnic National University |
Bibliographic description (Ukraine): | Різник В. В. Комбінаторний метод мінімізації булевих функцій / В. В. Різник, М. Т. Соломко // Вісник Національного університету «Львівська політехніка». Серія: Комп’ютерні системи та мережі. — Львів : Видавництво Львівської політехніки, 2017. — № 881. — С. 135–151. |
Bibliographic description (International): | Riznyk V. V. Combinatorial method of minimizing boolean functions / V. V. Riznyk, M. T. Solomko // Visnyk Natsionalnoho universytetu "Lvivska politekhnika". Serie: Kompiuterni systemy ta merezhi. — Lviv : Vydavnytstvo Lvivskoi politekhniky, 2017. — No 881. — P. 135–151. |
Is part of: | Вісник Національного університету «Львівська політехніка». Серія: Комп’ютерні системи та мережі, 881, 2017 |
Journal/Collection: | Вісник Національного університету «Львівська політехніка». Серія: Комп’ютерні системи та мережі |
Issue: | 881 |
Issue Date: | 28-Mar-2017 |
Publisher: | Видавництво Львівської політехніки |
Place of the edition/event: | Львів |
UDC: | 519.718 |
Keywords: | булева функція метод мінімізації мінімізація логічної функції блок-схема з повторенням мінтерми суперсклеювання змінних boolean function method of minimizing minimization of logic function block-design with repetition minterms super-sticking of variables |
Number of pages: | 17 |
Page range: | 135-151 |
Start page: | 135 |
End page: | 151 |
Abstract: | Розглянуто нову процедуру алгебри логіки – суперсклеювання змінних, яка
здійснюється за наявності у структурі таблиці істинності повної бінарної комбінаторної
системи з повторенням або неповної бінарної комбінаторної системи з повторенням.
Ефективність алгебричної операції суперсклеювання змінних істотно спрощує алгоритм
мінімізації булевих функцій, що уможливлює мінімізацію функцій з кількістю змінних
до 10. Considered the new procedure of logic algebra – super-sticking of variables, which is carried out in the presence of a truth table in complete binary combinatorial system with a repetition or incomplete of the system considered. The efficiency of the algebraic operation of super-sticking variables greatly simplifies the algorithm for minimizing boolean functions, which allows manual minimization of the functions. |
URI: | https://ena.lpnu.ua/handle/ntb/42834 |
Copyright owner: | © Національний університет „Львівська політехніка“, 2017 © Різник В. В., Соломко М. Т., 2017 |
URL for reference material: | https://en.wikipedia.org/wiki/Quine%E2 http://journals.uran.ua/tarp/article/view/108532 http://research.ijcaonline.org/volume82/number4/pxc3892127.pdf http://dspace.nbuv.gov.ua/handle/123456789/87194 http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412 https://www.researchgate.net/publication/268270733_Software_for_The_Minimization_of_The_Combinational_Logic_Functions_SOFTWARE_FOR_THE_MINIMIZATION_OF_THE_COMBINATIONAL_LOGIC_FUNCTIONS http://aircconline.com/ijma/V3N2/3211ijma04.pdf https://pdfs.semanticscholar.org/c53d/2240a2aa5531832a7707ad186dee23129ed8.pdf http://waprogramming.com/papers/50ae59d04ee143.95681909.pdf http://radio-best.cf/informatsiya/67-bunyak-a-elektronika-ta-mikroskhemotekhnika-2001-djvu-otsifrovano-gurtom http://nbuv.gov.ua/UJRN/VNULPPT_2013_766_6 http://stu.scask.ru/book_pta.php?id=62 http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412?nee http://cyclowiki.org/wiki/%D0 https://ru.wikipedia.org/w/index.php?oldid=36798414 |
References (Ukraine): | 1. Quine–McCluskey algorithm [Electronic resource]. – Access mode: https://en.wikipedia.org/wiki/Quine%E2 %80 %93McCluskey_algorithm – 15.10.2017. – Title from the screen. 2. Riznyk V. Minimization of boolean functions by combinatorial method [Теxt] / V. Riznyk, M. Solomko // Technology audit and production reserves. – Vol 4/2 (36), 2017. – P. 49–64. http://journals.uran.ua/tarp/article/view/108532 . 3. Riznyk V. Application of super-sticking algebraic operation of variables for boolean functions minimization by combinatorial method [Теxt] / V. Riznyk, M. Solomko // Technology audit and production reserves. – Vol. 6 (38), 2017. P. 50 – 66. 4. Manojlović, Vladislav (2013) Minimization of Switching Functions using Quine-McCluskey Method. International Journal of Computer Applications (0975 – 8887) Volume 82 – No 4, November 2013, 12–16. http://research.ijcaonline.org/volume82/number4/pxc3892127.pdf 5. Rytsar, Bohdan (2015) The Minimization Method of Boolean Functionns in Polynomial Set-theoretical Format. Conference: Proc.24th Inter. Workshop, CS@P’2015, Sept. 28-30, 2015, 130–146 pp. (17), At Rzeszow, Poland, Volume: vol.2 http://dspace.nbuv.gov.ua/handle/123456789/87194 6. Rathore, T. S. (2014) Minimal Realizations of Logic Functions Using Truth Table Method with Distributed Simplification. IETE JOURNAL OF EDUCATION, Vol. 55, Nо. 1, JAN_JUN 2014, 26–32 http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412 7. Dan, Rotar (2010) Software for The Minimization of The Combinational Logic Functions. The Romanian Review Precision Mechanics, Optics & Mechatronics,2010 (20), No. 37, 95–99. https://www.researchgate.net/publication/268270733_Software_for_The_Minimization_of_The_Combinational_Logic_Functions_SOFTWARE_FOR_THE_MINIMIZATION_OF_THE_COMBINATIONAL_LOGIC_FUNCTIONS 8. Zolfaghari, Behrouz, Sheidaeian, Hamed (2011) A NEW CASE FOR IMAGE COMPRESSION USING LOGIC FUNCTION MINIMIZATION. The International Journal of Multimedia & Its Applications (IJMA) Vol.3, No. 2, May 2011, 45–62. http://aircconline.com/ijma/V3N2/3211ijma04.pdf 9. Nosrati M., Karimi R., Nariri M. (2012) MINIMIZATION OF BOOLEAN FUNCTIONS USING GENETIC ALGORITHM. Anale. Seria Informatica. Vol. X fasc. 1 – 2012, 73–77. https://pdfs.semanticscholar.org/c53d/2240a2aa5531832a7707ad186dee23129ed8.pdf 10. Nosrati M., Karimi R. (2011) An Algorithm for Minimizing of Boolean Functions Based on Graph DS. World Applied Programming, Vol (1), No. (3),August 2011. 209–214. http://waprogramming.com/papers/50ae59d04ee143.95681909.pdf 11. Bunyak,A. Electronics and chip technology [Electronic resource] / A. Bunyak – Kyiv: View. “Aston”, 2001. – 385 p. – Access mode: http://radio-best.cf/informatsiya/67-bunyak-a-elektronika-ta-mikroskhemotekhnika-2001-djvu-otsifrovano-gurtom – Title from the screen. 12. Rytsar, B. Ye. Minimization of the system of logical functions by the method of parallel decoupling of conjunctures [Теxt] / B. Ye. Rytsar // Bulletin of the “Lviv Polytechnic” National University. Radio Electronics and Telecommunications. – 2013. – No. 766. – P. 18–27. – Access mode: http://nbuv.gov.ua/UJRN/VNULPPT_2013_766_6 . 13. Rytsar, B. Ye. New minimization method of logical functions in polynomial set-theoretical format. 1. Generalized rules of conjuncterms simplification / B. Ye. Rytsar // Control systems and machines. 2015. № 2. P. 39–57. – Available at: \www/URL: http://dspace.nbuv.gov.ua/handle/123456789/87194. 14. Samofalov, K. G. Applied theory of digital automata [Electronic resource] / K. G. Samofalov, A. M. Romlinkevich, V. N. Valuisky, Yu. S. Kanevsky, M. M. Pinevich – К.: Vishcha shk. Head Publishing House, 1987. – 375 p. – Access mode: http://stu.scask.ru/book_pta.php?id=62 – 15. 12. 2017. – Title from the screen. 15. Rathore T. S. (2014) Minimal Realizations of Logic Functions Using Truth Table Method with Distributed Simplification / T. S. Rathore // IETE Journal of Education, 55:1, 26–32, DOI: 21412.http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412?nee dAccess=true 16. The three-dimensional map of Carnot [Electronic resource] – Access mode: http://cyclowiki.org/wiki/%D0 %A2 %D1 %80 %D1 %91 %D1 %85 %D0 %BC%D0 %B5 %D1 %80 %D0 %BD%D0 %B0 %D1 %8F_%D0 %BA%D0 %B0 %D1 %80 %D1 %82 %D0 %B0_%D0 %9A%D0 %B0 %D1 %80 %D0 %BD%D0 %BE – 15. 10. 2017. – Title from the screen. 17. Map of Carnot [Electronic resource] – Access mode: https://ru.wikipedia.org/w/index.php?oldid=36798414 – 15. 10. 2017. – Title from the screen. |
References (International): | 1. Quine–McCluskey algorithm [Electronic resource], Access mode: https://en.wikipedia.org/wiki/Quine%E2 %80 %93McCluskey_algorithm – 15.10.2017, Title from the screen. 2. Riznyk V. Minimization of boolean functions by combinatorial method [Text], V. Riznyk, M. Solomko, Technology audit and production reserves, Vol 4/2 (36), 2017, P. 49–64. http://journals.uran.ua/tarp/article/view/108532 . 3. Riznyk V. Application of super-sticking algebraic operation of variables for boolean functions minimization by combinatorial method [Text], V. Riznyk, M. Solomko, Technology audit and production reserves, Vol. 6 (38), 2017. P. 50 – 66. 4. Manojlović, Vladislav (2013) Minimization of Switching Functions using Quine-McCluskey Method. International Journal of Computer Applications (0975 – 8887) Volume 82 – No 4, November 2013, 12–16. http://research.ijcaonline.org/volume82/number4/pxc3892127.pdf 5. Rytsar, Bohdan (2015) The Minimization Method of Boolean Functionns in Polynomial Set-theoretical Format. Conference: Proc.24th Inter. Workshop, CS@P’2015, Sept. 28-30, 2015, 130–146 pp. (17), At Rzeszow, Poland, Volume: vol.2 http://dspace.nbuv.gov.ua/handle/123456789/87194 6. Rathore, T. S. (2014) Minimal Realizations of Logic Functions Using Truth Table Method with Distributed Simplification. IETE JOURNAL OF EDUCATION, Vol. 55, No. 1, JAN_JUN 2014, 26–32 http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412 7. Dan, Rotar (2010) Software for The Minimization of The Combinational Logic Functions. The Romanian Review Precision Mechanics, Optics & Mechatronics,2010 (20), No. 37, 95–99. https://www.researchgate.net/publication/268270733_Software_for_The_Minimization_of_The_Combinational_Logic_Functions_SOFTWARE_FOR_THE_MINIMIZATION_OF_THE_COMBINATIONAL_LOGIC_FUNCTIONS 8. Zolfaghari, Behrouz, Sheidaeian, Hamed (2011) A NEW CASE FOR IMAGE COMPRESSION USING LOGIC FUNCTION MINIMIZATION. The International Journal of Multimedia & Its Applications (IJMA) Vol.3, No. 2, May 2011, 45–62. http://aircconline.com/ijma/V3N2/3211ijma04.pdf 9. Nosrati M., Karimi R., Nariri M. (2012) MINIMIZATION OF BOOLEAN FUNCTIONS USING GENETIC ALGORITHM. Anale. Seria Informatica. Vol. X fasc. 1 – 2012, 73–77. https://pdfs.semanticscholar.org/P.53d/2240a2aa5531832a7707ad186dee23129ed8.pdf 10. Nosrati M., Karimi R. (2011) An Algorithm for Minimizing of Boolean Functions Based on Graph DS. World Applied Programming, Vol (1), No. (3),August 2011. 209–214. http://waprogramming.com/papers/50ae59d04ee143.95681909.pdf 11. Bunyak,A. Electronics and chip technology [Electronic resource], A. Bunyak – Kyiv: View. "Aston", 2001, 385 p, Access mode: http://radio-best.cf/informatsiya/67-bunyak-a-elektronika-ta-mikroskhemotekhnika-2001-djvu-otsifrovano-gurtom – Title from the screen. 12. Rytsar, B. Ye. Minimization of the system of logical functions by the method of parallel decoupling of conjunctures [Text], B. Ye. Rytsar, Bulletin of the "Lviv Polytechnic" National University. Radio Electronics and Telecommunications, 2013, No. 766, P. 18–27, Access mode: http://nbuv.gov.ua/UJRN/VNULPPT_2013_766_6 . 13. Rytsar, B. Ye. New minimization method of logical functions in polynomial set-theoretical format. 1. Generalized rules of conjuncterms simplification, B. Ye. Rytsar, Control systems and machines. 2015. No 2. P. 39–57, Available at: \www/URL: http://dspace.nbuv.gov.ua/handle/123456789/87194. 14. Samofalov, K. G. Applied theory of digital automata [Electronic resource], K. G. Samofalov, A. M. Romlinkevich, V. N. Valuisky, Yu. S. Kanevsky, M. M. Pinevich – K., Vishcha shk. Head Publishing House, 1987, 375 p, Access mode: http://stu.scask.ru/book_pta.php?id=62 – 15. 12. 2017, Title from the screen. 15. Rathore T. S. (2014) Minimal Realizations of Logic Functions Using Truth Table Method with Distributed Simplification, T. S. Rathore, IETE Journal of Education, 55:1, 26–32, DOI: 21412.http://www.tandfonline.com/doi/pdf/10.1080/09747338.2014.921412?nee dAccess=true 16. The three-dimensional map of Carnot [Electronic resource] – Access mode: http://cyclowiki.org/wiki/%D0 %A2 %D1 %80 %D1 %91 %D1 %85 %D0 %BC%D0 %B5 %D1 %80 %D0 %BD%D0 %B0 %D1 %8F_%D0 %BA%D0 %B0 %D1 %80 %D1 %82 %D0 %B0_%D0 %9A%D0 %B0 %D1 %80 %D0 %BD%D0 %BE – 15. 10. 2017, Title from the screen. 17. Map of Carnot [Electronic resource] – Access mode: https://ru.wikipedia.org/w/index.php?oldid=36798414 – 15. 10. 2017, Title from the screen. |
Content type: | Article |
Appears in Collections: | Комп'ютерні системи та мережі. – 2017. – №881 |
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2017n881_Riznyk_V_V-Combinatorial_method_of_135-151.pdf | 1.54 MB | Adobe PDF | View/Open | |
2017n881_Riznyk_V_V-Combinatorial_method_of_135-151__COVER.png | 381.2 kB | image/png | View/Open |
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