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Journal Article

Some Remarks on Boolean Sums

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Mehlhorn, K. (1979). Some Remarks on Boolean Sums. Acta Informatica, 12, 371-375.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-AF87-1
Abstract
Summary  Neciporuk, Lamagna/Savage and Tarjan determined the monotone network complexity of a set of Boolean sums if any two sums have at most one variable in common. Wegener then solved the case that any two sums have at most k variables in common. We extend his methods and results and consider the case that any set of h +1 distinct sums have at most k variables in common. We use our general results to explicitly construct a set of n Boolean sums over n variables whose monotone complexity is of order n 5/3. The best previously known bound was of order n 3/2. Related results were obtained independently by Pippenger. This paper was presented at the MFCS 79 Symposium, Olomouc, Sept. 79