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## High-Level Replacement Systems applied to Algebraic Specifications and Petri Nets.

Ehrig, Hartmut;
Gajewsky, Maike;
Parisi-Presicce, Francesco
In:
Ehrig, H.; Kreowski, H.-J.; Montanari, U.; G. Rozenberg: *Handbook of Graph Grammars and Computing by Graph Transformation, Vol. III: Concurrency, Parallelism, and Distribution*, pages 341-400.
September 1999.

Abstract:
The general idea of high-level replacement systems is to generalize the
concept of graph transformation systems and graph grammars from graphs to
all kinds of structures which are of interest in Computer Science and
Mathematics. Within the algebraic approach of graph transformation this is
possible by replacing graphs, graph morphisms, and pushouts (gluing) of
graphs by objects, morphisms, and pushouts in a suitable category. Of
special interest are categories for all kinds of labelled and typed
graphs, hypergraphs, algebraic specifications and Petri nets. In this
chapter, we show how some basic results for graph transformation systems
in the algebraic double pushout approach can be reformulated in the
framework of high-level replacement systems. The specific choice of
results concerning local Church-Rosser properties and horizontal
structuring is motivated by the results needed in our application areas
studied in this contribution. In order to show the great variety of the
high-level replacement approach we do not consider specific graphs and
graph transformation but algebraic specifications and Petri nets as
application domains, where transformation corresponds to rule-based
changes of the structure of specifications and nets, respectively. The
first application shows how high-level replacement systems can be
instantiated by algebraic specifications. An algebraic transformation rule
corresponds to the interface part of an algebraic module specification for
software systems. This allows applying high-level replacement techniques
to software system design. As an application it is shown how to reuse an
algebraic module specification of an airport schedule for the design of a
book library. The second main application shows how rule-based
modification of Petri nets can be considered as a special case of
high-level replacement techniques. An important result is the
compatibility of horizontal structuring of nets with rule-based
modification. This result is essential within a case study of a medical
information system where the functional essence is developed by rule-based
modification from the actual state of the system represented by algebraic
high-level nets.

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