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Acta Informatica

, Volume 13, Issue 2, pp 109–114 | Cite as

A new lower bound on the monotone network complexity of Boolean sums

  • Ingo Wegener
Article

Summary

Neciporuk [3], Lamagna/Savage [1] and Tarjan [6] determined the monotone network complexity of a set of Boolean sums if each two sums have at most one variable in common. By this result they could define explicitely a set of n Boolean sums which depend on n variables and whose monotone complexity is of order n3/2. In the main theorem of this paper we prove a more general lower bound on the monotone network complexity of Boolean sums. Our lower bound is for many Boolean sums the first nontrivial lower bound. On the other side we can prove that the best lower bound which the main theorem yields is the n3/2-bound cited above. For the proof we use the technical trick of assuming that certain functions are given for free.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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.
    Lamagna, E.A., Savage, J.E.: Combinational complexity of some monotone functions. 15th SWAT Conference, New Orleans, pp 140–144, 1974Google Scholar
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    Mehlhorn, K., Galil, Z.: Monotone switching circuits and Boolean matrix product. Computing 16, 99–111 (1976)MathSciNetCrossRefGoogle Scholar
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    Neciporuk, E.I.: On a Boolean matrix. Systems Research Theory 21, 236–239 (1971)MathSciNetGoogle Scholar
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    Pippenger, N.: On another Boolean matrix. IBM Research Report RC 6914, 1977Google Scholar
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    Savage, J.E.: An algorithm for the computation of linear forms. SIAM J. Comput. 3, 150–158 (1974)MathSciNetCrossRefGoogle Scholar
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    Tarjan, R.E.: Complexity of monotone networks for computing conjunctions. Preprint, Computer Science Department, Stanford UniversityGoogle Scholar
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    Wegener, I.: Switching functions whose monotone complexity is nearly quadratic. Theor. Comput. Sci. 9 (in press 1979)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Ingo Wegener
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1Germany

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