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IEEE Trans Neural Netw. 2010 Apr;21(4):584-94. doi: 10.1109/TNN.2009.2039802. Epub 2010 Feb 17.

State-space analysis of Boolean networks.

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Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China.


This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recent work on the topic: Using semitensor product of matrices and the matrix expression of logic, the logical dynamic equations of Boolean (control) networks can be converted into standard discrete-time dynamics. To use the state-space approach, the state space and its subspaces of a Boolean network have been carefully defined. The basis of a subspace has been constructed. Particularly, the regular subspace, Y-friendly subspace, and invariant subspace are precisely defined, and the verifying algorithms are presented. As an application, the indistinct rolling gear structure of a Boolean network is revealed.

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