Computational Complexity of Synchronization under Sparse Regular Constraints
Abstract
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under supervisory control. Here, we study the computational complexity of this problem for the class of sparse regular constraint languages. We give a new characterization of sparse regular sets, which equal the bounded regular sets, and derive a full classification of the computational complexity of CSP for letterbounded regular constraint languages, which properly contain the strictly bounded regular languages. Then, we introduce strongly selfsynchronizing codes and investigate CSP for bounded languages induced by these codes. With our previous result, we deduce a full classification for these languages as well. In both cases, depending on the constraint language, our problem becomes NPcomplete or polynomial time solvable.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2108.00081
 Bibcode:
 2021arXiv210800081H
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Computational Complexity;
 Electrical Engineering and Systems Science  Systems and Control;
 68Q45 (Primary) 68Q19 (Secondary);
 F.4.3;
 F.1.3
 EPrint:
 Accepted at FCT 2021, see https://www.corelab.ntua.gr/fct2021/