An in-between "implicit" and "explicit" complexity: Automata

TL;DR

This paper surveys how automata theory has contributed to implicit computational complexity by providing machine-dependent models with implicit bounds, focusing on the interplay between automata and complexity measures.

Contribution

It offers a comprehensive overview of automata-based approaches to implicit computational complexity, highlighting their role in internalizing complexity bounds.

Findings

Automata theory provides machine-dependent models with implicit bounds.

Automata contribute to internalizing complexity measures.

Survey clarifies automata's role in implicit computational complexity.

Abstract

Implicit Computational Complexity makes two aspects implicit, by manipulating programming languages rather than models of com-putation, and by internalizing the bounds rather than using external measure. We survey how automata theory contributed to complexity with a machine-dependant with implicit bounds model.