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Computer Science > Formal Languages and Automata Theory

arXiv:2108.00081 (cs)
[Submitted on 30 Jul 2021]

Title:Computational Complexity of Synchronization under Sparse Regular Constraints

Authors:Stefan Hoffmann
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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.
Comments: Accepted at FCT 2021, see this https URL
Subjects: Formal Languages and Automata Theory (cs.FL); Computational Complexity (cs.CC); Systems and Control (eess.SY)
MSC classes: 68Q45 (Primary) 68Q19 (Secondary)
ACM classes: F.4.3; F.1.3
Cite as: arXiv:2108.00081 [cs.FL]
  (or arXiv:2108.00081v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.2108.00081

Submission history

From: Stefan Hoffmann [view email]
[v1] Fri, 30 Jul 2021 21:09:01 UTC (387 KB)
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