Topological structure of implicit Boolean networks

In this study, implicit Boolean networks (IBNs), which are more general than classic BNs, are proposed for the first time motivated by the river-crossing decision problem. By resorting to the admissible set, some necessary and sufficient conditions are established, under which IBNs can be equivalently converted into classic BNs or restricted BNs. Subsequently, an improved approach is presented to determine the topological structure of dynamic-algebraic BNs (D-ABNs), based on which transformation relations between IBNs and D-ABNs are given. Finally, a biochemical oscillator example is used to show the application of the obtained results.