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Acta Informatica

, Volume 20, Issue 1, pp 103–111 | Cite as

On sets of Boolean n-vectors with all k-projections surjective

  • Ashok K. Chandra
  • Lawrence T. Kou
  • George Markowsky
  • Shmuel Zaks
Article

Summary

Given a set, S, of Boolean n-vectors, one can choose k of the n coordinate positions and consider the set of k-vectors which results by keeping only the designated k positions of each vector, i.e., from k-projecting S. In this paper, we study the question of finding sets S as small as possible such that every k-projection of S yields all the 2 k possible k-vectors. We solve this problem constructively and almost optimally for k=2 and all n. For k≧3, the constructive solutions we describe are much larger than an O(k 2 k log n) nonconstructive upper bound which we derive. The nonconstructive approach allows us to generate fairly small sets S which have a very high probability of having the surjective k-projection property.

Keywords

Information System Operating System Data Structure High Probability Communication Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Birkhoff, G.: Lattice Theory. Am. Math. Soc., Providence, Rhode Island, 1967Google Scholar
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    Chandra, A.K., Kou, L.T., Markowsky, G., Zaks, S.: On sets of Boolean n-vectors with all k-projections surjective. Technical report RC 8936, IBM Research, Yorktown Heights, July 1981Google Scholar
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    Tang, D.T., Woo, L.S.: Exhaustive test pattern generation with constant weight vectors. Technical report RC 9442, IBM Research, Yorktown Heights, June 1982Google Scholar
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    Tang, D.T., Chen, C.L.: Personal communication, Aug. 1982Google Scholar
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    Kleitman, D.J., Spencer, J.: Families of k-independent sets. Discrete Math. 6, 255–262 (1973)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Ashok K. Chandra
    • 1
  • Lawrence T. Kou
    • 2
  • George Markowsky
    • 1
  • Shmuel Zaks
    • 3
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  2. 2.Electrical and Computer Engineering DepartmentUniversity of CaliforniaDavisUSA
  3. 3.TechnionHaifaIsrael

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