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Encoding the dynamics of deterministic systems

by Torres, L. M., Wagler, A. K..

Series: 2009-29, Preprints

05C65 Hypergraphs
05C75 Structural characterization of families of graphs

We present a model for the dynamics of discrete deterministic systems, based on an extension of the Petri nets framework. Our model relies on the definition of a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The structure of this conflict graph is discussed in the context of hypergraph theory and particular properties related to some specific classes of dynamic systems are investigated. Moreover, we provide a characterization in terms of a local consistency condition of those deterministic systems whose dynamic behavior can be encoded using our approach. Finally, we consider the problem of recognizing when an orientation of the transition conflict graph is valid for encoding the dynamic behavior of a system.

Petri nets, deterministic systems, hypergraphs