TR18-020 Authors: Meena Mahajan, Prajakta Nimbhorkar, Anuj Tawari

Publication: 30th January 2018 08:56

Downloads: 149

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We study computation by formulas over $(min, +)$. We consider the computation of $\max\{x_1,\ldots,x_n\}$

over $\mathbb{N}$ 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.