Observability of boolean networks is NP-hard

Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables and Boolean outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We study the control-theoretic notion of observability, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. We show that the problem of determining whether a BN is observable or not is NP-hard. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graph-theoretic approach.