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We present an algebraic approach to reveal attractor transitions in Boolean networks under single control based on the recently developed matrix semitensor product theory. In this setting, the reachability of attractors is estimated by the state transition matrices. We then propose procedures that compute the shortest control sequence and the result of each step of input (control) exactly. The general derivation is exemplified by numerical simulations for two kinds of gene regulation networks, the protein-nucleic acid interactions network and the cAMP receptor of Dictyostelium discoideum network.

Stability of nonlinear feedback shift registers SCIENCE CHINA Information Sciences 59, 012204 (2016); Decomposition of nonlinear feedback shift registers based on Boolean networks SCIENCE CHINA Information Sciences 62, 039110 (2019); A novel synthesis method for reliable feedback shift registers via Boolean networks SCIENCE CHINA Information Sciences EUCLIDEAN ALGORITHM FOR MULTISEQUENCES SHIFT REGISTER SYNTHESIS