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## An Algebraic Semantics for Hierarchical P/T Nets.

Basten, T.;
Voorhoeve, M.
In:
*Proceeding of the 16th International Conference on Application and Theory of Petri Nets, Turin, June 1995.*, pages 45-65.
1995.

Abstract:
The first part of this paper gives an algebraic sematnics for
Place/Transition nets in terms of an algebra which is based on the process
algebra ACP. The algebraic semantics is such that aP/T net and its term
representation have the same operational behavior. As opposed to other
approaches in the literature, the actions in the algebra do not correspond
to the firing of a transition, but to the consumption or production of
tokens. Equality to P/T nets can be determined in a purely equational way.
The second part of this paper extends the results to hierarchical P/T
nets. It gives a compositional algebraic semantics for both their complete
operational behavior and their high-level, observable behavior. By means
of a non-trivial example, the Alternating-Bit Protocol, it is shown that
the notions of abstraction and verification in the process algebra ACP can
be used to verify in an equational way whether a hierarchical P/T net
satisfies some algebraic specification of its observable behavior. Thus,
the theory in this paper can be used to determine whether two hierarchical
P/T nets have the same observable behavior. As an example, it is shown
that the Alternating-Bit Protocol behaves as a simple one-place buffer.
The theory forms a basis for a modular, top-down design methodology based
on Petri nets.

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