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$\mathcal{M}$-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation

Published online by Cambridge University Press:  26 June 2014

HARTMUT EHRIG ,
ULRIKE GOLAS ,
ANNEGRET HABEL ,
LEEN LAMBERS  and
FERNANDO OREJAS
HARTMUT EHRIG
Affiliation:
Technische Universität Berlin, Berlin, Germany Email: ehrig@cs.tu-berlin.de
ULRIKE GOLAS
Affiliation:
Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany Email: golas@zib.de
ANNEGRET HABEL
Affiliation:
Universität Oldenburg, Oldenburg, Germany Email: habel@informatik.uni-oldenburg.de
LEEN LAMBERS
Affiliation:
Hasso-Plattner-Institut, Universität Potsdam, Potsdam, Germany Email: leen.lambers@hpi.uni-potsdam.de
FERNANDO OREJAS
Affiliation:
Universitat Politècnica de Catalunya, Barcelona, Spain Email: orejas@lsi.upc.edu
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Abstract

Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of $\mathcal{M}$-adhesive categories, where $\mathcal{M}$-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 4: Structure Transformation , August 2014 , 240406
Copyright
Copyright © Cambridge University Press 2014 

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