Computational Complexity of Synchronization under Regular Commutative Constraints
Abstract
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.
Cite
@article{arxiv.2005.04042,
title = {Computational Complexity of Synchronization under Regular Commutative Constraints},
author = {Stefan Hoffmann},
journal= {arXiv preprint arXiv:2005.04042},
year = {2020}
}
Comments
Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theorem