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## The Box Calculus: a New Causal Algebra with Multi-label Communication.

Best, Eike
In:
Rozenberg, G.: *Lecture Notes in Computer Science, Vol. 609; Advances in Petri Nets 1992*, pages 21-69.
Springer-Verlag,
1992.

Abstract:
A new Petri net calculus called the calculus of Petri Boxes is described.
It has been designed to allow reasoning about the structure of a net and
about the relationship between nets, and to facilitate the compositional
semantic translation of high level constructs such as blocks, variables
and atomic actions into elementary Petri nets. The calculus is located
`midway' in such a translation. This paper first defines an algebra of Box
expressions. A corresponding algebra of Boxes is then defined and used
compositionally as a semantic model of Box expressions. The two algebras
feature a general asynchronous communication operation extending that of
CCS. Synchronization is defined as a unary operator. The algebras also
include refinement, iteration and recursion. It is shown how they can be
used to describe data and blocks. As the main results of this paper, it is
proved that the Box algebra satisfies various desirable structural laws
and enjoys two important behavioral properties. The paper also contains an
example proof of a mutual exclusion protocol.

Keywords:
Petri Nets; Process Algebras; Compositional Semantics; Multiway
Synchronization; Refinement; Recursion; Data.

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