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## Kausalität, Nebenläufigkeit und Konflikt. Elementare Netzsysteme aus topologisch relationaler Sicht.

Haar, Stefan
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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