Observability and Reconstructibility of Probabilistic Boolean Networks

In this letter, observability and reconstructibility properties of probabilistic boolean networks (PBNs) on a finite time interval are addressed. By assuming that the state update follows a probabilistic rule, while the output is a deterministic function of the state, we investigate under what conditions the knowledge of the output measurements in [0,T] allows the exact identification either of the initial state or of the final state of the PBN. By making use of the algebraic approach to PBNs, the concepts of observability, weak reconstructibility, and strong reconstructibility are introduced and characterized. Set theoretic algorithms to determine all possible initial/final states compatible with the given output sequence are provided.