Anatoly D. Plotnikov's Publications
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Anatoly Plotnikov's Publications

Inventions

Books

1. Discrete Mathematics, Moscow, ``New knowledge'', (1-th edition) 2005. - 288 pp. (2-nd edition) 2006. - 304 pp. (3-th edition) 2008. - 320 pp.
http://www.wnk.biz/html/ru/info26.htm
2. Mathematical programming, Minsk, ``New knowledge'', (1-th edition) 2006, (2-nd edition) 2007. - 171 pp.
http://wnk.biz/booksmart/978-985-475-242-6.html
3. Calculus of approximations, Minsk, ``New knowledge'', 2007. - 174 pp.
http://wnk.biz/booksmart/978-985-475-283-9.html

The Scientific Papers List

I have the Scientific Papers:

In English:

  1. Experimental Algorithm for the Maximum Independent Set Problem.
    http://lanl.arxiv.org/abs/0706.3565.
  2. About presentation of a digraph by dim 2 poset. "Advanced Studies in Contemporary Mathematics" volume 12 (1), 2006, p. 55-60.
  3. The lower bound of the number of all-or-none DAGs. "Advanced Studies in Contemporary Mathematics" volume 12 (2), 2006, p. 323-326.
  4. A formal approach to the oDAG/POSET problem (2004)
    http://www.cumulativeinquiry.com/Problems/solut2.pdf
  5. A Logical Model of HCP. "International Journal of Mathematics and Mathematical Sciences", Vol. 26, issue 11, 2001. Hindawi Publishing Corporation.
  6. Formalization of the class of problems solvable by a nondeterministic Turing machine http://xxx.lanl.gov/abs/cs/9903012.
  7. A class of problems of NP to be worth to search an efficient solving algorithm.
    http://xxx.lanl.gov/abs/cs/9903010.
  8. Designing SAT for HCP. http://xxx.lanl.gov/abs/cs/9903006.
  9. The problems without lookahead. (manuscript)
  10. One criterion of existence of a hamiltonian cycle. "Reliable Computing journal", issue 2 , (1998), 199 - 202.
  11. About the finding of independent vertices of a graph, Journal "Kibernetika", No. 1, 1989, p. 119 - 121.
  12. Formalization of the Class of Problems Solvable by a Nondeterministic Turing Machine, "Cybernetics and Systems Analysis", Vol. 33, No. 5, (1997), 635 - 640.
  13. Set-theoretical properties of extreme combinatorial problems. "SouthWest Journal Pure and Applied Mathematics" (SWJPAM), Vol. No. 2, (1996), 11 - 28.
  14. Polynomial-time partition of a graph into cliques. "SouthWest Journal Pure and Applied Mathematics" (SWJPAM), Vol. No. 1, (1996), 16 - 21.

In Ukrainian:

  1. Using the covering trees for building a Hamiltonian cycle. Journal "Measuring and computing devices in technological processes", 2(12), 2000, Khmelnitsky, p. 143 - 146.
  2. The dual problems of combinatorial optimization. Journal "News of the VPI", No. 3, 1995, p. 55 - 58.
  3. One approach to search of a Hamiltonian cycle in a graph. Journal "News of the VPI", No. 1, 1995, p. 65 - 69.
  4. The normal form of an extreme combinatorial problems. Journal "News of the VPI", No. 3, 1994, p. 73 - 76.
  5. To a question about minimization of Boolean functions. Journal "News of the VPI", No. 2,1994, p. 89 - 92.
  6. About partition of a graph into the minimum number cliques. Journal "News of the VPI", No. 1, 1993, p. 91 - 96.

In Russian:

  1. Some features of analysis of the symmetric cryptosystems
    "Information safety", 2010, No. 1(3), p. 107 - 111. (coauthor Petrov A.S.).
  2. Logical approach to the analysis of symmetric cryptosystem.
    "News of ENU in the name V. Dal", 2010, No. 3 (145), p. 311 - 319. (co-author Petrov A.S.).
  3. About complexity of algorithms and programs. 2002, 23 pp. http://homepages.compuserve.de/chasluebeck/dn/complex.rar
  4. A logical model of HCP. Journal "Discrete analysis and operations research", 2000, Novosibirsk, p. 101.
  5. Clarifying the class of the problems solvable by nondeterministic Turing machine. "Kibernetika i Sistemny Analiz", No. 5, 1997, p. 30 - 36.
  6. Some properties of the extreme combinatorial problems. In collection "Mathematical and program methods of designing information and of control systems", 1990, Penza, p. 14 - 15.
  7. About problem of a finding of independent set of the vertices in the graph. Journal "Kibernetika", No. 1, 1989, p. 119 - 121.
  8. About number of the Boolean matrices which is invariant rearrangements of lines. Journal "News of high schools. The mathematics.", No. 6, 1985, (co-author Mastiuk A.V.), pp. 1.
  9. The method of combinatorial optimization. Reports of Academy Sciences Ukraine, series "A", No. 2, 1981, pp. 4.
  10. To the minimization of bisum normal forms of the Boolean functions. Journal "Mathematical physics", issue 15, 1974 (co-author Manukyan V.A.), pp. 7.
  11. Application of interpolation to construction of minimum normal forms of the Boolean function. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, (co-author Manukyan V.A.), pp. 59 - 60.
  12. About algorithms of the functional separated decomposition. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, (co-author Polyakova T.D.), p. 59.
  13. The convolution of the L-functions. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, p. 58 - 59.
  14. The construction of minimum normal forms of the functions of 2m-valued logic. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, p. 58.
  15. About one approach to minimization of the Boolean functions. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, p. 57 - 58.
  16. Interpolation and minimization of some classes of the Boolean functions. Scientific-technical conference "Automation of technological preparation of manufacture in engineering by means of a computer", 1973, Voroshilovgrad, (co-author Manukyan V.A.), p. 57.
  17. About separated decomposition of boolean functions. Scientific-technical conference "Development and application of the computing machinery on microelectronic base", 1973, Severodonetsk, (co-author Polyakova T.D.), p. 1.
  18. The construction of the minimum DNF of the symmetrical boolean functions. Scientific-technical conference "Development and application of the computing machinery on microelectronic base", 1973, Severodonetsk, p. 1.
  19. Interpolation of a Boolean functions and its application. The preprint of Cybernetics Institute of Academy Sciences Ukraine, 1972, (co-author Manukyan V.A.), pp. 27.
  20. The use of the Boolean functions in computing machinery. The Informational Center of Coal Ministry of Ukraine, No. 2 - 4 (149), 1972, (co-author Manukyan V.A.), pp. 6.
  21. Analytical representation of the 2m-valued logic functions. In collection: "Multiciphered elements and their application", Soviet radio, 1971, 88 - 94.
  22. Theory of consecutive discrete transducers of the information. Scientific-technical conference "Development and application of facilities of computer machinery", Severodonetsk, 1969, p. 1.
  23. The questions of the functional synthesis of discrete transducers of the information of a word - word type. Doctor's dissertation, Kharkov, 1968, pp. 160.
  24. To the synthesis of discrete transducers converters of the information. Scientific-technical conference "Application of methods of the cybernetics for the solution of problems of the control", Kharkov, 1968 (co-author Rvachov V.L.), pp. 4.
  25. The machine for the centralized control. In collection: "Computing machinery", Kiev, 1968 (co-authors Velikikh N.P., Tarasenko A.N., Tarasyuk S.F.), 3 - 6.
  26. To the discrete information transducer theory. Scientific-technical conference "Development and application of a computing facilities and of an automatics", 1968, Severodonetsk, p. 1
  27. The use of a redundant notation for digital computer. In collection: "Mechanization and automation of the control", issue 4, 1968 (co-authors Kostelyansky V.M., Rozenfeld T.K.), pp. 3
  28. The machine for the centralized control of technological process of smelting in open-hearth furnaces. In collection: "Devices and facility of automation", issue 2, 1968, (co-authors Velikikh N.P., Tarasenko A.N., Tarasyuk S.F.), pp. 4.
  29. The multichannel system for processing of signals of the frequent sensors. In collection: "Technical systems of data processing", Institute of cybernetics of Academy of Sciences of Ukraine, issue 1, 1968, (co-authors Velikikh N.P., Tarasenko A.N., Tarasyuk S.F.), pp. 12
  30. About the functional completeness for a system of logic operations which are determined on the set of m-capacity binary numbers. Journal "Devices and facility of automatics" (Kharkov State University), issue 6, 1967, p. 28 - 32.
  31. Discrete setting of the shaft by the shortest way. Journal "Devices and facility of automation", issue 5, 1965, p. 3
  32. The specialized computing device. Journal "Automatics and device-building", No. 2, 1965, (co-authors Afanasev V.A., Kazais E.B.), p. 17 - 19.
  33. The floating-point parallel-serial arithmetic unit. The report of the Research Institute of Control Computers (RICC), Severodonetsk, 1963, pp. 17.
  34. The parallel-serial computing unit. The report of the Research Institute of Control Computers (RICC), Severodonetsk, 1963, pp. 63.
  35. The floating-point arithmetic unit. The report of the Research Institute of Control Computers (RICC), Severodonetsk, 1963, pp. 12.

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