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Fixed Point Preserving Model Reduction of Boolean Networks Focusing on Complement and Absorption Laws

Fuma MOTOYAMA, Koichi KOBAYASHI, Yuh YAMASHITA

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Summary :

A Boolean network (BN) is well known as a discrete model for analysis and control of complex networks such as gene regulatory networks. Since complex networks are large-scale in general, it is important to consider model reduction. In this paper, we consider model reduction that the information on fixed points (singleton attractors) is preserved. In model reduction studied here, the interaction graph obtained from a given BN is utilized. In the existing method, the minimum feedback vertex set (FVS) of the interaction graph is focused on. The dimension of the state is reduced to the number of elements of the minimum FVS. In the proposed method, we focus on complement and absorption laws of Boolean functions in substitution operations of a Boolean function into other one. By simplifying Boolean functions, the dimension of the state may be further reduced. Through a numerical example, we present that by the proposed method, the dimension of the state can be reduced for BNs that the dimension of the state cannot be reduced by the existing method.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.5 pp.721-728
Publication Date
2023/05/01
Publicized
2022/10/24
Online ISSN
1745-1337
DOI
10.1587/transfun.2022MAP0009
Type of Manuscript
Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
Category

Authors

Fuma MOTOYAMA
  Hokkaido University
Koichi KOBAYASHI
  Hokkaido University
Yuh YAMASHITA
  Hokkaido University

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