Reisig, W.: Edition Versal, pages 1-305. Berlin: Dieter Bertz Verlag, 1998.
Abstract: Elementary Net Systems or ENS consist of a net formed by places and transitions together with a set of marked places. To understand the semantics - that is, the behavior in time - of ENS, the structure of process nets derived from the system can be investigated using partial order theory. Here, the reverse approach is taken: We start with the structural investigation of standard nets - causal nets - whose behavior can be well analyzed because of their non-branching and acyclic structure. In fact, we work with two classes of relations - for causality and concurrency -, both derived from an underlying partial order. Using the formal tool of relational quotients, we successively extend the relational approach to more general classes of nets; in doing so, we ensure the inheritance of essential behavioral properties, in particular, safety, (weak) liveness and resettability (wherever applicable). Along with this, a corresponding notion of well-formedness will be characterized by the net class generated by our construction. This construction process successively takes us to several focuses of investigation. One is the theory of cyclic orders, where new insights into their theory are gained by the quotient approach; another the structural and semantical properties of branching. We discuss the value of introducing relations to describe alternataives and arrive at the conclusion that such relations are most fruitful on the second level, i.e. as relations among sets of net elements rather than on the level of places and transitions themselves.
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