Meena Mahajan, Prajakta Nimbhorkar, Anuj Tawari

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 ...
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Meena Mahajan, Prajakta Nimbhorkar, Anuj Tawari

We study bounded depth $(\min, +)$ formulas computing the shortest path polynomial. For depth $2d$ with $d \geq 2$, we obtain lower bounds parametrized by certain fan-in restrictions on all $+$ gates except those at the bottom level. For depth $4$, in two regimes of the parameter, the bounds are ... more >>>