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vol 67 / April, 2024
Article

DOI 10.17586/0021-3454-2022-65-7-478-491

UDC 62-507.15

COMPLEXITY OF ARBITRARY FUNCTIONS OF THE LOGIC ALGEBRA OF A SMALL NUMBER OF VARIABLES

O. N. Muzychenko
Research and Production Firm Meridian JSC; Chief Designer of Information Control Systems;


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Abstract. A method for evaluating the complexity of arbitrary function of Boolean algebra is examined, based on presenting such a function as a composition of monotone functions. Accurate upper estimates have been received for the complexity of monotone and arbitrary functions depending on a small number of variables.
Keywords: monotone and arbitrary logic functions, complexity

References:
  1. Shannon C.E. Bell System Technical Journal, 1948, no. 3(July).
  2. Lupanov O.B. Problemy kibernetiki, 1963, no. 10, pp. 88–96. (in Russ.)
  3. Korshunov A.D. Russian Mathematical Surveys, 2003, no. 5, pp. 929–1001.
  4. Ugol'nikov A.B. Problemy kibernetiki, 1976, no. 31, pp. 167–185. (in Russ.)
  5. Pippenger N. Math. Systems Theory, 1977/78, vol. 11, рр. 289–316.
  6. Lupanov O.B. Problemy kibernetiki, 1965, no. 14, pp. 31–110. (in Russ.)
  7. Muzychenko O.N. Spetsializirovannyye metody sinteza logicheskikh skhem. Chast' 1. Metody sinteza logicheskikh skhem simmetrichnykh i porogovykh funktsiy (Specialized Methods for Synthesizing Logic Circuits. Part 1. Methods for Synthesizing Logic Circuits of Symmetric and Threshold Functions), St. Petersburg, 2004, 161 р. (in Russ.)
  8. Muzychenko O.N. Metody sinteza logicheskikh skhem (Methods for Synthesizing Logic Circuits), St. Petersburg, 2018, 860 р. (in Russ.)
  9. Pospelov D.A. Logicheskiye metody analiza i sinteza skhem (Logical Methods of Analysis and Synthesis of Circuits), Moscow, 1974, 368 р. (in Russ.)
  10. Muzychenko O.N. Russian Mathematics, 2017, no. 7, pp. 35–42.
  11. Karpova N.A. Problemy kibernetiki, 1973, no. 26, pp. 53–94. (in Russ.)
  12. Muzychenko O.N. Automation and Remote Control, 1994, no. 12, pp. 117–128. (in Russ.)
  13. Korshunov A.D. Soviet Mathematics. Doklady, 1977, no. 4(233), pp. 543–546. (in Russ.)
  14. Korshunov A.D. Problemy kibernetiki, 1981, no. 38, pp. 5–108. (in Russ.)
  15. Muzychenko O.N., Lukoyanov V.P. Questions of radio electronics. General questions of radio electronics, 1984, no. 12, pp. 120–128. (in Russ.)