English

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 kk 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}
}