Hidden Markov processes in the context of symbolic dynamics

TL;DR

This paper explores hidden Markov processes within symbolic dynamics, providing background, tools, literature review, and open problems to foster interdisciplinary understanding and progress.

Contribution

It offers a comprehensive overview of hidden Markov processes in symbolic dynamics, highlighting their properties, methods, and unresolved questions.

Findings

Survey of existing literature and tools

Identification of open problems in the field

Clarification of the relationship between hidden Markov processes and sofic measures

Abstract

In an effort to aid communication among different fields and perhaps facilitate progress on problems common to all of them, this article discusses hidden Markov processes from several viewpoints, especially that of symbolic dynamics, where they are known as sofic measures, or continuous shift-commuting images of Markov measures. It provides background, describes known tools and methods, surveys some of the literature, and proposes several open problems.