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Parallelism and concurrency in high-level replacement systems

Published online by Cambridge University Press:  04 March 2009

Hartmut Ehrig ,
Annegret Habel ,
Hans-Jörg Kreowski  and
Francesco Parisi-Presicce
Hartmut Ehrig
Affiliation:
Technical University of Berlin, Berlin, Germany
Annegret Habel
Affiliation:
University of Bremen, Bremen, Germany
Hans-Jörg Kreowski
Affiliation:
University of Bremen, Bremen, Germany
Francesco Parisi-Presicce
Affiliation:
University of L'Aquila, L'Aquila, Italy
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Abstract

High-level replacement systems are formulated in an axiomatic algebraic framework based on categories pushouts. This approach generalizes the well-known algebraic approach to graph grammars and several other types of replacement systems, especially the replacement of algebraic specifications which was recently introduced for a rule-based approach to modular system design.

in this paper basic notions like productions, derivations, parellel and sequential independence are introduced for high-level replacement syetms leading to Church-Rosser, Parallelism and concurrency Theorems previously shown in the literature for special cases only. In the general case of high-level replacement systems specific conditions, called HLR1- and HLR2-conditions, are formulated in order to obtain these results.

Several examples of high-level replacement systems are discussed and classified w.r.t. HLR1- and HLR2-conditions showing which of the results are valid in each case.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 1 , Issue 3 , November 1991 , pp. 361 - 404
Copyright
Copyright © Cambridge University Press 1991

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