@article{EhrigGolasHabeletal.2014,
  author    = {Ehrig, Hartmut and Golas, Ulrike and Habel, Annegret and Lambers, Leen and Orejas, Fernando},
  title     = {M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation},
  series = {Mathematical structures in computer science : a journal in the applications of categorical, algebraic and geometric methods in computer science},
  volume    = {24},
  journal   = {Mathematical structures in computer science : a journal in the applications of categorical, algebraic and geometric methods in computer science},
  number    = {4},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0960-1295},
  doi       = {10.1017/S0960129512000357},
  pages     = {48},
  year      = {2014},
  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 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.},
  language  = {en}
}
@article{EhrigGolasHabeletal.2012,
  author    = {Ehrig, Hartmut and Golas, Ulrike and Habel, Annegret and Lambers, Leen and Orejas, Fernando},
  title     = {M-Adhesive Transformation Systems with Nested Application Conditions Part 2: Embedding, Critical Pairs and Local Confluence},
  series = {Fundamenta informaticae},
  volume    = {118},
  journal   = {Fundamenta informaticae},
  number    = {1-2},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0169-2968},
  doi       = {10.3233/FI-2012-705},
  pages     = {35 -- 63},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@misc{EhrigGolasHabeletal.2014,
  author    = {Ehrig, Hartmut and Golas, Ulrike and Habel, Annegret and Lambers, Leen and Orejas, Fernando},
  title     = {M-adhesive transformation systems with nested application conditions},
  series = {Postprints der Universit{\"a}t Potsdam : Digital Engineering Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Digital Engineering Reihe},
  number    = {001},
  doi       = {10.25932/publishup-41565},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-415651},
  pages     = {50},
  year      = {2014},
  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 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.},
  language  = {en}
}
@article{GolasLambersEhrigetal.2012,
  author    = {Golas, Ulrike and Lambers, Leen and Ehrig, Hartmut and Orejas, Fernando},
  title     = {Attributed graph transformation with inheritance: Efficient conflict detection and local confluence analysis using abstract critical pairs},
  series = {THEORETICAL COMPUTER SCIENCE},
  volume    = {424},
  journal   = {THEORETICAL COMPUTER SCIENCE},
  publisher = {ELSEVIER SCIENCE BV},
  address   = {AMSTERDAM},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2012.01.032},
  pages     = {46 -- 68},
  year      = {2012},
  abstract  = {Inheritance is an important and widely spread concept enabling the elegant expression of hierarchy in object-oriented software programs or models. It has been defined for graphs and graph transformations enhancing the applicability of this formal technique. Up to now, for the analysis of transformations with inheritance a flattening construction has been used, which yields all the well-known results for graph transformation but results in a large number of graphs and rules that have to be analyzed. In this paper, we introduce a new category of typed attributed graphs with inheritance. For the detection of conflicts between graph transformations on these graphs, the notion of abstract critical pairs is defined. This allows us to perform the analysis on polymorphic rules and transformations without the need for flattening, which significantly increases the efficiency of the analysis and eases the interpretation of the analysis results. The new main result is the Local Confluence Theorem for typed attributed graph transformation with inheritance using abstract critical pairs. All constructions and results are demonstrated on an example for the analysis of refactorings. (C) 2012 Elsevier B.V. All rights reserved.},
  language  = {en}
}