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Motivated by safety-critical applications in cyber-physical systems, in thispaper we study the notion of critical observability and design of observers fornetworks of Finite State Machines (FSMs). Critical observability is a propertyof FSMs that corresponds to the possibility of detecting if the current stateof an FSM belongs to a set of critical states modeling operations that may beunsafe or, in general, operations of specific interest in a particularapplication. A critical observer is an observer that detects on-line theoccurrence of critical states. When a large-scale network of FSMs isconsidered, the construction of such an observer is prohibitive because of thelarge computational effort needed. In this paper we propose a decentralizedarchitecture for critical observers of networks of FSMs, where on-linedetection of critical states is performed by local critical observers, eachassociated with an FSM of the network. For the efficient design ofdecentralized critical observers we first extend on-the-fly algorithmstraditionally used in the community of formal methods for the formalverification and control design of FSMs. We then extend to networks of FSMs,bisimulation theory traditionally given in the community of formal methods forsingle FSMs. The proposed techniques provide a remarkable computationalcomplexity reduction, as discussed throughout the paper and also demonstratedby means of illustrative examples. Finally, we propose an example in thecontext of biological networks, which illustrates the applicability of ourresults and also the interest arising from concrete application domains.

Decentralized Critical Observers of Networks of Finite State Machines and Model Reduction