An Algebra of Petri Nets with Arc-Based Time Restrictions

In this paper we present two algebras, one based on term re-writing and the other on Petri nets, aimed at the specification and analysis of concurrent systems with timing information. The former is based on process expressions (at-expressions) and employs a set of SOS rules providing their operational semantics. The latter is based on a class of Petri nets with time restrictions associated with their arcs, called at-boxes, and the corresponding transition firing rule. We relate the two algebras through a compositionally defined mapping which for a given at-expression returns an at-box with behaviourally equivalent transition system. The resulting model, called the Arc Time Petri Box Calculus (atPBC), extends the existing approach of the Petri Box Calculus (PBC).

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