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On the Minimal Controllability of Boolean Networks With k-Regular Dependency Graphs

  • Christopher H. Fok
  • Chi-Wing Wong
  • Wai-Ki Ching
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Abstract

Boolean networks (BNs) are widely used to model gene regulatory networks and other biological systems. In this paper, we investigate the minimal controllability problem for BNs subject to degree constraints. We first establish three new best-case upper bounds for XOR-BNs whose dependency graphs are k-regular. We then introduce classes of BNs that are invariant under cyclically partite transformation (CPT-invariant) and prove theorems connecting BN controllability with the surjectivity of vector-valued Boolean functions. Finally, by combining an analysis of this surjectivity with a probabilistic argument, we derive a new general lower bound on the minimum number of control nodes required for majority-type threshold BNs with (2k+1)-regular dependency graphs.

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Cite

BibTeXRIS
BibTeX
@misc{fok2026minimal,
  title = {{On the Minimal Controllability of Boolean Networks With $k$-Regular Dependency Graphs}},
  author = {Christopher H. Fok and Chi-Wing Wong and Wai-Ki Ching},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08101},
  eprint = {2611.08101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08101},
}
RIS
TY  - UNPB
TI  - On the Minimal Controllability of Boolean Networks With k-Regular Dependency Graphs
AU  - Christopher H. Fok
AU  - Chi-Wing Wong
AU  - Wai-Ki Ching
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08101
UR  - https://arxiv.org/abs/2611.08101
AB  - Boolean networks (BNs) are widely used to model gene regulatory networks and other biological systems. In this paper, we investigate the minimal controllability problem for BNs subject to degree constraints. We first establish three new best-case upper bounds for XOR-BNs whose dependency graphs are k-regular. We then introduce classes of BNs that are invariant under cyclically partite transformation (CPT-invariant) and prove theorems connecting BN controllability with the surjectivity of vector-valued Boolean functions. Finally, by combining an analysis of this surjectivity with a probabilistic argument, we derive a new general lower bound on the minimum number of control nodes required for majority-type threshold BNs with (2k+1)-regular dependency graphs.
ER  -