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  • 标题:Computing the maximum using ( min + ) formulas
  • 本地全文:下载
  • 作者:Meena Mahajan ; Prajakta Nimbhorkar ; Anuj Tawari
  • 期刊名称:Electronic Colloquium on Computational Complexity
  • 印刷版ISSN:1433-8092
  • 出版年度:2018
  • 卷号:2018
  • 出版社:Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
  • 摘要:

    We study computation by formulas over ( min + ) . We consider the computation of max x 1 x n over N as a difference of ( min + ) formulas, and show that size n + n log n is sufficient and necessary. Our proof also shows that any ( min + ) formula computing the minimum of all sums of n − 1 out of n variables must have n log n leaves; this too is tight. Our proofs use a complexity measure for ( min + ) functions based on minterm-like behaviour and on the entropy of an associated graph.

  • 关键词:circuits ; formulas ; lower bounds ; tropical semiring
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