Lower Bounds for Tropical Circuits and Dynamic Programs

TL;DR

This paper investigates the computational limits of tropical circuits, which are closely related to dynamic programming, by establishing lower bounds that highlight their limitations compared to other circuit models.

Contribution

It introduces new lower bound arguments for tropical circuits, advancing understanding of their computational complexity and limitations.

Findings

Established lower bounds for tropical circuits

Demonstrated limitations of dynamic programming algorithms

Bridged understanding between tropical and other circuit models

Abstract

Tropical circuits are circuits with Min and Plus, or Max and Plus operations as gates. Their importance stems from their intimate relation to dynamic programming algorithms. The power of tropical circuits lies somewhere between that of monotone boolean circuits and monotone arithmetic circuits. In this paper we present some lower bounds arguments for tropical circuits, and hence, for dynamic programs.