Finite automata approach to observability of switched Boolean control networks

In this paper, the observability of switched Boolean control networks (SBCNs) is determined. First, a new concept of weighted pair graphs for SBCNs is defined. Second, the weighted pair graph is used to transform an SBCN into a deterministic finite automaton (DFA). Lastly, the observability of the SBCN is determined by testing the completeness of the DFA. Based on these results, algorithms for determining the observability and the initial state are designed. The computational complexity of this algorithm is doubly exponential in the number of nodes of SBCNs. Furthermore, more effective sufficient or necessary conditions for the observability of SBCNs are obtained directly from weighted pair graphs. The computational complexity of these conditions is exponential in the number of nodes of SBCNs.