Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents
Abstract
For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for commutative automata over an arbitrary alphabet and automata with simple idempotents over a binary alphabet as input automata. The latter class contains, for example, the \v{C}ern\'y family of automata. We find that for commutative input automata, the problem is always solvable in polynomial time, for every constraint language. For input automata with simple idempotents over a binary alphabet and with a constraint language given by a partial automaton with up to three states, the constrained synchronization problem is also solvable in polynomial time.
Cite
@article{arxiv.2109.02743,
title = {Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents},
author = {Stefan Hoffmann},
journal= {arXiv preprint arXiv:2109.02743},
year = {2021}
}