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Non-Pure Nets and Their Transition

This paper extends the theory of regions developed by Nielsen, Rozenberg and Thiagarajan within a set-theoretic framework, to accommodate the class of non-pure nets and their transition systems. Those are called semi-elementary nets and semi-elementary transition systems, respectively. The main motivation of such an extension is practical, the need to model asyn-chronous hardware structures, where certain events happen only when some conditions (these are called co-conditions) are true but without changing the state of these conditions. One of the applications of this theory is synthesis of Petri net models from state-based speciications. As an example we present a Petri net model of control of a counterrow pipeline for Sproull's asynchronous processor. This control was originally speciied as a transition system which did not satisfy elementarity axioms of Nielsen et al.