Further Results on the Controllability of Boolean Control Networks

This note presents further results based on the recent paper [J. Liang, H. Chen, and J. Lam, “An improved criterion for controllability of Boolean control networks,” <italic>IEEE Trans. Autom. Control</italic>, vol. 62, no. 11, pp. 6012–6018, Nov. 2017]. After some optimizations, the conventional method can be more efficient than the method used in the above paper. We also propose an improved method via combining the well known Tarjan's algorithm and depth-first search technique for the controllability analysis of Boolean control networks (BCNs). As a result, the computational complexity will not exceed <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> with <inline-formula><tex-math notation="LaTeX">$N=2^n$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of state-variables in a BCN.

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