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Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach
 HANDBOOK OF GRAPH GRAMMARS AND COMPUTING BY GRAPH TRANSFORMATION, VOLUME 1: FOUNDATIONS
, 1996
"... ..."
Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations
 Inform. and Comput
, 1998
"... A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with reg ..."
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Cited by 46 (20 self)
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A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular lookahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular lookahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular lookahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...
Shapely Hierarchical Graph Transformation
 Journal of Computer and System Sciences
, 2001
"... Diagrams can be represented by graphs, and the animation and transformation of diagrams can be modeled by graph transformation. This paper studies extensions of graphs and graph transformation that are important for programming with graphs: ..."
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Cited by 43 (11 self)
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Diagrams can be represented by graphs, and the animation and transformation of diagrams can be modeled by graph transformation. This paper studies extensions of graphs and graph transformation that are important for programming with graphs:
An Algebraic Presentation of Term Graphs, via GSMonoidal Categories
 Applied Categorical Structures
, 1999
"... . We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the wellknown characterisation of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particula ..."
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Cited by 37 (24 self)
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. We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the wellknown characterisation of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particular, we show that term graphs over a signature \Sigma are onetoone with the arrows of the free gsmonoidal category generated by \Sigma. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator r), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of r and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively. Keywords: algebraic theories, directed acyclic graphs, gsmonoidal categories, symmetric monoidal categories, term graphs. Mathematical Subject Clas...
An Inductive View of Graph Transformation
 In Workshop on Algebraic Development Techniques
, 1998
"... . The dynamic behavior of rulebased systems (like term rewriting systems [24], process algebras [27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result i ..."
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Cited by 30 (12 self)
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. The dynamic behavior of rulebased systems (like term rewriting systems [24], process algebras [27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result is built: This is the role played by (the application of) a substitution in term rewriting. Or inductively, showing how to build the class of all possible reductions from a set of basic ones: For term rewriting, this is the usual definition of the rewrite relation as the minimal closure of the rewrite rules. As far as graph transformation is concerned, the operational view is by far more popular: In this paper we lay the basis for the orthogonal view. We first provide an inductive description for graphs as arrows of a freely generated dgsmonoidal category. We then apply 2categorical techniques, already known for term and term graph rewriting [29, 7], recasting in this framework the...
Decidability of the Finiteness of Ranges of Tree Transductions
 Inform. and Comput
, 1996
"... . The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an elem ..."
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Cited by 17 (7 self)
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. The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an element of a given algebra. A sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for TBY + definable sets and for the ranges of TBY + computable relations. The obtained result applies in particular to the class of string languages that can be defined by TBY + transductions via the yield mapping. This is a large class which is proved to form a substitutionclosed full AFL. 1 Introduction The finiteness problem is one of the classical decidability problems in formal language theory. For a given language of interest, one usually does not wish to know whether that language is finite (because it usually is not), but rather whether the l...
Hypergraphs as a Uniform Diagram Representation Model
 UNIVERSITY OF PADERBORN
, 1998
"... When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are wellknown concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagra ..."
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Cited by 11 (5 self)
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When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are wellknown concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relationships between components. This paper also proposes a procedure for translating diagrams into their hypergraph model, i.e., a graphical scanner, and a procedure to check the hypergraph against a hypergraph grammar defining the diagrams' syntax, i.e., a parsing procedure. Such procedures are necessary to make use of such a hypergraph model in visual environments that support freehand editing where the user can modify diagrams arbitrarily.
A Graphical Specification of Model Transformations with Triple Graph Grammars
 In First European Conference Model Driven Architecture  Foundations and Applications, number 3748 in Lecture Notes in Computer Science
, 2005
"... Abstract. Models and model transformations are the core concepts of OMG’s MDA T M approach. Within this approach, most models are derived from the MOF and have a graphbased nature. In contrast, most of the current model transformations are specified textually. To enable a graphical specification of ..."
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Cited by 11 (0 self)
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Abstract. Models and model transformations are the core concepts of OMG’s MDA T M approach. Within this approach, most models are derived from the MOF and have a graphbased nature. In contrast, most of the current model transformations are specified textually. To enable a graphical specification of model transformation rules, this paper proposes to use triple graph grammars as declarative specification formalism. These triple graph grammars can be specified within the FUJABA tool and we argue that these rules can be more easily specified and they become more understandable and maintainable. To show the practicability of our approach, we present how to generate Tefkat rules from triple graph grammar rules, which helps to integrate triple graph grammars with a state of a art model transformation tool and shows the expressiveness of the concept. 1
Categorical Approach to Horizontal Structuring and Refinement of HighLevel Replacement Systems
 APPLIED CATEGORICAL STRUCTURES
, 1998
"... Based on the wellknown theory of highlevel replacement systems  a categorical formulation of graph grammars  we present new results concerning refinement of highlevel replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of re ..."
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Cited by 10 (6 self)
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Based on the wellknown theory of highlevel replacement systems  a categorical formulation of graph grammars  we present new results concerning refinement of highlevel replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. This concept is called Qtransformations and is established within the framework of highlevel replacement systems. The main idea is to supply rules with an additional morphism, which belongs to a specific class Q of morphisms. This leads to the new notions of Qrules and Qtransformations. Moreover, several concepts and results of highlevel replacement systems are extended to Qtransformations. These are sequential and parallel transformations, union, and fusion, based on different colimit constructions. The main results concern the compatibility of these constructions with Qtransformations that is the corresponding theorems for usual transformations are extended to Qtransform...