Domain and Event Structure Semantics
for Petri Nets with Read and Inhibitor Arcs

P. Baldan (1), N. Busi (2), A. Corradini (1) and G. M. Pinna (3)

(1) Dipartimento di Informatica - Università  di Pisa
(2) Dipartimento di Scienze dell'Informazione - Università di Bologna
(3) Dipartimento di Matematica - Università di Siena

Abstract:

We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work of Winskel on safe nets and extending a previous work in [BCM] for nets with read arcs, the truly concurrent semantics is given at a categorical level via a chain of functors leading from the category SW-IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains (equivalent to the category PES of prime event structures). As an intermediate semantic model, we introduce inhibitor event structures, an extension of prime event structures able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs.

 

[BCM] P. Baldan, A. Corradini, and U. Montanari.
           An event structure semantics for P/T contextual nets: Asymmetric event structures
           In M. Nivat, editor, Proceedings of FoSSaCS '98, volume 1378 of LNCS. Springer Verlag, 1998.