Complexity of checking whether two automata are synchronized by the same language

TL;DR

This paper investigates the computational complexity of determining whether two automata share the same set of reset words, establishing that this problem is PSPACE-complete, which indicates high computational difficulty.

Contribution

It proves that checking the equivalence of reset word languages for two automata is PSPACE-complete, highlighting the problem's computational hardness.

Findings

The problem is PSPACE-complete.

Reset word language equivalence is computationally hard.

Implications for automata synchronization analysis.

Abstract

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.