@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}
}
@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}
}