Download PDF

Cybernetics and Systems Analysis

, Volume 42, Issue 3, pp 311–319 | Cite as

Statement and solution of some problems on a mathematical safe

  • G. A. Donets
  • Bin Zhan
Open Access
Cybernetics
Received:

Abstract

The problem on a mathematical safe is formulated and studied in terms of graph theory. The cases of simplest digraphs such as paths, contours, and doubly connected components are analyzed. A number of statements on the existence of solutions to these problems are proved. The results obtained are extended to the case of corresponding nondirected graphs.

Keywords

mathematical safe set of locks dependency matrix of locks solution of a system of equations final state of a safe residue class 
Download to read the full article text

References

  1. 1.
    G. A. Donets, “Solution of one problem on a safe,” in: Intern. Conf. on Applied Mathematics Dedicated to the 65th Anniversary of B. N. Pshenichnyi (June 25–28, 2000), Kyiv (2000), p. 39.Google Scholar
  2. 2.
    A. P. Ventura, “How to turn all the lights out,” Elem. Math., 55, 135–141 (2000).MathSciNetCrossRefGoogle Scholar
  3. 3.
    T. R. Walsh, “Cracking Saferacker,” J. Recreat. Math., 17, No. 4, 117–128 (1984–1985).Google Scholar
  4. 4.
    G. A. Donets “Solution of the safe problem on (0,1)-matrices,” Kibern. Sist. Anal., No. 1, 98–105 (2002).Google Scholar
  5. 5.
    S. L. Kryvyi, “Methods of solution and criteria of compatibility of systems of linear Diophantine equations over the set of natural numbers,” Kibern. Sist. Anal., No. 4, 12–36 (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • G. A. Donets
    • 1
  • Bin Zhan
    • 1
  1. 1.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

Personalised recommendations