Conversion between Logic and Algebraic Expressions of Boolean Control Networks

The conversion between logic and algebraic expressions of Boolean control networks plays a worthy role in the analysis and design of digital circuits. In this paper, for a single Boolean function, a direct conversion between the minterm canonical form and the structure matrix is provided. For a Boolean control network consisting of systems of Boolean functions, two algorithms are developed to achieve the mutual conversion between the logic and algebraic expressions. The presented algorithms decrease exponentially the complexity of the semi-tensor product based method. Some numerical examples are given to demonstrate the algorithms and to compare our method with the existing ones.

Reachability and Controllability Analysis of Periodic Switched Boolean Control Networks

The reachability and controllability of switched Boolean (control) network are discussed in this paper. Based on semi-tensor product, using the vector form of Boolean logical variable, the switched Boolean (control) network is expressed as a discrete time system with state and control variables. For the switched Boolean network without control, the stabilization by suitable switching signal is discussed. Also, the controllability of the periodic switching signal is learned, and the conditions for stability and controllability of periodic switched Boolean networks avoiding states setCare obtained.