Siphon-based characterization of liveness and liveness-enforcing supervision for sequential resource allocation systems

One of the most interesting developments from, both, a theoretical and a practical perspective, in the emerging theory of resource allocation systems (RAS), is the characterization of the non-liveness of many RAS classes through the Petri net (PN)-based structural object of empty, or more generally, deadly marked siphon. The work presented in this paper seeks to develop a general theory that provides a unifying framework for all the relevant existing results, and reveals the key structures and mechanisms that connect the RAS non-liveness to the concept of deadly marked – and in certain cases, empty – siphon. In this capacity, the presented results allow also the extension of the siphon-based characterization of non-liveness to broader RAS classes, and provide a clear and intuitive explanation for the limitations of the approach. The last part of the work discusses how the derived structural characterization of RAS non-liveness can be combined with some algorithms for detecting empty or deadly marked siphons in a given PN marking, in order to develop analytical liveness sufficiency tests and systematic procedures for the design of liveness-enforcing supervisors (LES).