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 letter-bounded regular constraint languages, which properly contain the strictly bounded regular languages. Then, we introduce strongly self-synchronizing 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 NP-complete or polynomial time solvable.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2108.00081
- arXiv:
- arXiv:2108.00081
- Bibcode:
- 2021arXiv210800081H
- Keywords:
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- 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
- E-Print:
- Accepted at FCT 2021, see https://www.corelab.ntua.gr/fct2021/