Universal algorithms for solving the matrix Bellman equations over semirings

TL;DR

This survey reviews universal algorithms for solving matrix Bellman equations over various semirings, highlighting original algorithms, applications, and software implementations in tropical and idempotent semirings.

Contribution

It provides a comprehensive overview of existing algorithms and introduces new methods for solving matrix Bellman equations over semirings.

Findings

Overview of universal algorithms for semiring Bellman equations

Introduction of original algorithms for specific semirings

Discussion of applications and software implementations

Abstract

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed.