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## Petri Nets over Partial Algebra.

Desel, Jörg;
Juhás, Gabriel;
Lorenz, Robert
In:
H. Ehrig, G. Juhás, J. Padberg, G. Rozenberg (Eds.): *LNCS 2128: Unifying Petri Nets - Advances in Petri Nets*, pages 126-pp.
Springer Verlag,
December 2001.

Abstract:
Partial algebra is a suitable tool to define sequential semantics for
arbitrary restrictions of the occurrence rule, such as capacity or context
restrictions. This paper focuses on non-sequential process semantics of
Petri nets over partial algebras. It is shown that the concept of partial
algebra is suitable as a basis for process construction of different
classes of Petri nets taking dependencies between processes that restrict
concurrent composition into consideration. Thus, Petri nets over partial
algebra provide a unifying framework for Petri net classes in which some
processes cannot be executed concurrently, such as elementary nets with
context. We will illustrate this claim proving a one-to-one correspondence
between processes constructed using partial algebra and processes based on
partial orders for elementary nets with context. Furthermore, we provide
compositional process term semantics using the presented framework for
place/transition nets with (both weak and strong) capacities and
place/transition nets with inhibitor arcs.

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