TY  - JOUR
A1  - Ehrig, Hartmut
A1  - Golas, Ulrike
A1  - Habel, Annegret
A1  - Lambers, Leen
A1  - Orejas, Fernando
T1  - M-Adhesive Transformation Systems with Nested Application Conditions  Part 2: Embedding, Critical Pairs and Local Confluence
JF  - Fundamenta informaticae
N2  - Graph transformation systems have been studied extensively and applied to several areas of computer science like formal language theory, the modeling of databases, concurrent or distributed systems, and visual, logical, and functional programming. In most kinds of applications it is necessary to have the possibility of restricting the applicability of rules. This is usually done by means of application conditions. In this paper, we continue the work of extending the fundamental theory of graph transformation to the case where rules may use arbitrary (nested) application conditions. More precisely, we generalize the Embedding theorem, and we study how local confluence can be checked in this context. In particular, we define a new notion of critical pair which allows us to formulate and prove a Local Confluence Theorem for the general case of rules with nested application conditions. All our results are presented, not for a specific class of graphs, but for any arbitrary M-adhesive category, which means that our results apply to most kinds of graphical structures. We demonstrate our theory on the modeling of an elevator control by a typed graph transformation system with positive and negative application conditions.
KW  - M-adhesive transformation systems
KW  - M-adhesive categories
KW  - graph replacement categories
KW  - nested application conditions
KW  - embedding
KW  - critical pairs
KW  - local confluence
Y1  - 2012
U6  - https://doi.org/10.3233/FI-2012-705
SN  - 0169-2968
VL  - 118
IS  - 1-2
SP  - 35
EP  - 63
PB  - IOS Press
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Ehrig, Hartmut
A1  - Golas, Ulrike
A1  - Habel, Annegret
A1  - Lambers, Leen
A1  - Orejas, Fernando
T1  - M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation
JF  - Mathematical structures in computer science : a journal in the applications of categorical, algebraic and geometric methods in computer science
N2  - 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 M-adhesive categories, where 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.
Y1  - 2014
U6  - https://doi.org/10.1017/S0960129512000357
SN  - 0960-1295
SN  - 1469-8072
VL  - 24
IS  - 4
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - GEN
A1  - Ehrig, Hartmut
A1  - Golas, Ulrike
A1  - Habel, Annegret
A1  - Lambers, Leen
A1  - Orejas, Fernando
T1  - M-adhesive transformation systems with nested application conditions
BT  - Part 1: parallelism, concurrency and amalgamation
T2  - Postprints der Universität Potsdam : Digital Engineering Reihe
N2  - 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 M-adhesive categories, where 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Reihe der Digital Engineering Fakultät - 1 
KW  - level-replacement systems
KW  - graph-transformations
KW  - distributed systems
KW  - synchronization
KW  - confluence
KW  - categories
KW  - programs
KW  - grammars
KW  - model
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-415651
IS  - 001
ER  -