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Please use this identifier to cite or link to this item: 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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