Reset Complexity of Ideal Languages

TL;DR

This paper introduces the concept of reset complexity for ideal languages, establishing bounds and relationships with state complexity, and exploring automata that achieve minimal reset complexity.

Contribution

It defines reset complexity, compares it with state complexity, and investigates automata with minimal reset complexity for ideal languages.

Findings

Bounds on reset complexity in terms of state complexity

Comparison between reset and state complexity for certain languages

Analysis of automata with minimal reset complexity

Abstract

We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state complexity for languages related to slowly synchronizing automata and study uniqueness question for automata yielding the minimum of reset complexity.