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Main Title: Multi-amalgamation of rules with application conditions in M-adhesive categories
Author(s): Golas, Ulrike
Habel, Annegret
Ehrig, Hartmut
Type: Article
Language Code: en
Abstract: Amalgamation is a well-known concept for graph transformations that is used to model synchronised parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalisation of the operational semantics of statecharts and other visual modelling languages, where typed attributed graphs are used for multiple rules with nested application conditions. However, the theory of amalgamation for the double-pushout approach has so far only been developed on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, in the current paper we present the theory of amalgamation for M-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions. The two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem, which generalises the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronised parallelism. In order to apply the largest amalgamated rule, we use maximal matchings, which are computed according to the actual instance graph. The constructions are illustrated by a small but meaningful running example, while a more complex case study concerning the firing semantics of Petri nets is presented as an introductory example and to provide motivation.
Issue Date: 2014
Date Available: 23-Nov-2017
DDC Class: 004 Datenverarbeitung; Informatik
Journal Title: Mathematical structures in computer science
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 24
Issue: 4
Article Number: e240405
Publisher DOI: 10.1017/s0960129512000345
EISSN: 1469-8072
ISSN: 0960-1295
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Softwaretechnik und Theoretische Informatik » Publications

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