D-continuous causal nets: a model of non-sequential processes

Abstract

We propose a model of non-sequential processes and study its properties. The model is called D-continuous causal nets (CCN's) and is based on a class of Petri nets. A causal net is essentially a partially ordered set of conditions and events which represents a fragment of the history of a concurrent system. D-continuity is a generalization of Dedekind's definition of the continuity (completeness) of the reals which is applicable to both totally and partially ordered sets as also to both dense and discrete structures. We develop a number of properties of our model and discuss why these might be useful properties for a non-sequential process to have.