Petri nets are monoids: a new algebraic foundation for net theory
Meseguer, J.
Montanari, U.
SRI Int., Menlo Park, CA;
This paper appears in: Logic in Computer Science, 1988. LICS '88., Proceedings of the Third Annual Symposium on
Publication Date: 5-8 Jul 1988
On page(s): 155-164
Meeting Date: 07/05/1988 - 07/08/1988
Location: Edinburgh, UK
ISBN: 0-8186-0853-6
References Cited: 22
INSPEC Accession Number: 3248156
Digital Object Identifier: 10.1109/LICS.1988.5114
Current Version Published: 2002-08-06
Abstract
The composition and extraction mechanisms of Petri nets are at
present inadequate. This problem is solved by viewing place/transition
Petri nets as ordinary, directed graphs equipped with two algebraic
operations corresponding to parallel and sequential composition of
transitions. A distributive law between the two operations captures a
basic fact about concurrency. Novel morphisms are defined, mapping
single, atomic transitions into whole computations, thus relating system
descriptions at different levels of abstraction. Categories equipped
with products and coproducts (corresponding to parallel and
nondeterministic compositions) are introduced for Petri nets with and
without initial markings. It is briefly indicated how the approach
yields function spaces and novel interpretations of duality and
invariants. The results provide a formal basis for expressing the
semantics of concurrent languages in terms of Petri nets and an
understanding of concurrency in terms of algebraic structures over
graphs and categories that should apply to other models and contribute
to the conceptual unification of concurrency
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