Ideal Separation and General Theorems for Constrained Synchronization and their Application to Small Constraint Automata
Abstract
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the computational complexity. Additionally, we state a theorem giving PSPACE-hardness that broadly generalizes previously used constructions and a result on how to combine languages by concatenation to get polynomial time solvable constrained synchronization problems. We use these results to give a classification of the complexity landscape for small constraint automata of up to three states.
Cite
@article{arxiv.2005.05907,
title = {Ideal Separation and General Theorems for Constrained Synchronization and their Application to Small Constraint Automata},
author = {Stefan Hoffmann},
journal= {arXiv preprint arXiv:2005.05907},
year = {2021}
}
Comments
Complete reworking of the 1st version. The classification of the 1st version is achieved by identifying and utilising more general theorems, which are also stated in the work