Complexity of limit cycles with block-sequential update schedules in conjunctive networks
Discrete Mathematics
2022-03-23 v1 Computational Complexity
Abstract
In this paper, we deal the following decision problem: given a conjunctive Boolean network defined by its interaction digraph, does it have a limit cycle of a given length k? We prove that this problem is NP-complete in general if k is a parameter of the problem and in P if the interaction digraph is strongly connected. The case where is a constant, but the interaction digraph is not strongly connected remains open. Furthermore, we study the variation of the decision problem: given a conjunctive Boolean network, does there exist a block-sequential (resp. sequential) update schedule such that there exists a limit cycle of length k? We prove that this problem is NP-complete for any constant k >= 2.
Keywords
Cite
@article{arxiv.2203.11361,
title = {Complexity of limit cycles with block-sequential update schedules in conjunctive networks},
author = {Julio Aracena and Florian Bridoux and Luis Gómez and Lilian Salinas},
journal= {arXiv preprint arXiv:2203.11361},
year = {2022}
}