Rewriting Logic as a Unifying Framework for Petri Nets

We propose rewriting logic as a unifying framework for a wide range of Petri nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that “Petri nets are monoids” suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specifications. We furthermore generalize this result to a general form of algebraic net specifications subsuming also colored Petri nets as a special case. The soundness and completeness results we state relate the commutative process semantics of Petri nets proposed by Best and Devillers to the model-theoretic semantics of rewriting logic in the sense of natural isomorphisms between suitable functors. In addition we show how place/transition nets with test arcs and timed Petri nets can be equipped with a rewriting semantics and discuss how other extensions can be treated along similar lines. Beyon...

• Type: Conference
• Year: 2001
• Where: APN
• Authors: Mark-Oliver Stehr, José Meseguer, Peter Csaba Ölveczky
• Keywords: APN 2001, Artificial Intelligence, Petri Net, Place/transition Nets, Rewriting Logic