Observability of Boolean control networks: A unified approach based on the theories of finite automata

摘要

The problem on how to determine the observability of Boolean control networks(BCNs) has been open for five years already. In this paper, we propose aunified approach to determine all the four types of observability of BCNs inthe literature. We define the concept of weighted pair graphs for BCNs. In thesense of each observability, we use the so-called weighted pair graph totransform a BCN to a finite automaton, and then we use the automaton todetermine observability. In particular, the two types of observability thatrely on initial states and inputs in the literature are determined. Finally, weshow that no pairs of the four types of observability are equivalent, whichreveals the essence of nonlinearity of BCNs.