Invertibility and Nonsingularity of Boolean Control Networks

  • Kuize ZhangEmail author
  • Lijun Zhang
  • Lihua Xie
Part of the Communications and Control Engineering book series (CCE)


As stated before, initially a Boolean control network (BCN) (see \(\Sigma _1\) in Fig. 3.1) was in a state, then as inputs were fed into the BCN one by one, state transitions occurred successively, yielding a sequence of outputs. What may interest us is: Could the above process be reversed? That is, whether there exists another BCN (see \(\Sigma _2\) in Fig. 3.1) that reverses the inputs and outputs of \(\Sigma _1\). In this chapter, we prove a series of fundamental results on this problem, and apply these results to the mammalian cell cycle.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceKTH Royal Institute of TechnologyStockholmSweden
  2. 2.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina
  3. 3.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

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