Efficient Enumeration of Fixed Points in Complex Boolean Networks Using Answer Set Programming

Authors Van-Giang Trinh , Belaid Benhamou, Sylvain Soliman

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Author Details

Van-Giang Trinh
  • LIS, Aix-Marseille University, Marseille, France
Belaid Benhamou
  • LIS, Aix-Marseille University, Marseille, France
Sylvain Soliman
  • Lifeware team, Inria Saclay, Palaiseau, France

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Van-Giang Trinh, Belaid Benhamou, and Sylvain Soliman. Efficient Enumeration of Fixed Points in Complex Boolean Networks Using Answer Set Programming. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Boolean Networks (BNs) are an efficient modeling formalism with applications in various research fields such as mathematics, computer science, and more recently systems biology. One crucial problem in the BN research is to enumerate all fixed points, which has been proven crucial in the analysis and control of biological systems. Indeed, in that field, BNs originated from the pioneering work of R. Thomas on gene regulation and from the start were characterized by their asymptotic behavior: complex attractors and fixed points. The former being notably more difficult to compute exactly, and specific to certain biological systems, the computation of stable states (fixed points) has been the standard way to analyze those BNs for years. However, with the increase in model size and complexity of Boolean update functions, the existing methods for this problem show their limitations. To our knowledge, the most efficient state-of-the-art methods for the fixed point enumeration problem rely on Answer Set Programming (ASP). Motivated by these facts, in this work we propose two new efficient ASP-based methods to solve this problem. We evaluate them on both real-world and pseudo-random models, showing that they vastly outperform four state-of-the-art methods as well as can handle very large and complex models.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Logic programming and answer set programming
  • Applied computing → Computational biology
  • Applied computing → Systems biology
  • Computational systems biology
  • Boolean network
  • Fixed point
  • Answer set programming


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