Cybernetics and Systems Analysis

, Volume 36, Issue 1, pp 102–107 | Cite as

On estimation of the probability of absence of collisions of some random mappings

  • R. Gilchrist
  • I. N. Kovalenko
Systems Analysis


Let X and Y be finite sets and φ: (X,Y) →Y be a mapping. Consider a random mapping i → φ(xi,yi), where xi are arbitrarily chosen from the set X, whereas (yi) is a random sample from Y without replacement. A two-sided bound is derived for the probability of absence of collisions of this mapping. A case of mapping, defined as φ(x, y)=x+ y modulo n, is considered in particular. The results may be used in the selection of identification codes.


random mapping collision identification code 


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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • R. Gilchrist
    • 1
  • I. N. Kovalenko
    • 2
  1. 1.Research Center STORMNorth London UniversityGreat Britain
  2. 2.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

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