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

摘要

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