DREWES, F., KREOWSKI, H.-J., AND HABEL, A. Hyperedge replacement graph grammars. In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, G. Rozenberg, Ed. World Scientic, 1997, pp. 95 -- 162.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....E H are disjoint, for every graph H. Remark. In order to avoid confusion we remark that the hypergraphs used in the short version of this paper [14] come with an additional component, namely a sequence of distinguished nodes called points. These are useful in connection with hyperedge replacement [13], which is employed by the flattening process considered in Section 6. However, as long as one is not interested in flattening, and in particular as far as the basic theory is concerned, points are of no particular value they just complicate the whole theory in an unnecessary way. This is the ....

....GOE tOE HOE, where GOE, HOE, and tOE are the flattened versions of G, H, and t, respectively. Obviously, the converse cannot hold as structural information gets lost in the flattening process. For the definition of flattening, we extend the well known concept of hyperedge replacement (see [13, 25]) to hierarchical graphs. Let H be a hierarchical graph. For every set E E H of edges, H E denotes the hierarchical graph obtained by deleting all the edges in E from H, i.e. H E=OG, F H 0E, ctsP where G= OV H ,E H 0E, att, labP, att and lab being the restrictions of att H and lab H to E H 0E, ....

F. Drewes, A. Habel, and H.-J. Kreowski, Hyperedge replacement graph grammars, in Rozenberg [40, Chap. 2, pp. 95--162].

....c 2001 Published by Elsevier Science B. V. nested graphs are compositional since they forbid edges that cross component boundaries. Graph transformation is a rich theory for rule based computations on graphs [21] We combine simple concepts of graph transformation, like edge replacement [4] and substitutive transformation [19] to a new way of nested graph transformation that is based on variable matching and instantiation. We nd this intuitive, elegant, and particularly useful for programming, as it resembles other rule based computational models, e.g. term rewriting [15] ....

.... lists, root connected trees and the like [23] Here we devise a means to specify shapes of graphs in a way that is not possible on the level of imperative languages (nor in functional or logical languages where pointers are hidden altogether) The speci cation is based on edge replacement [4], but we immediately adopt a terminology tting to our purposes. 7 Shape Grammars. The handle graph of a label l 2 consists of one straight k ary l edge that is attached to k pairwise distinct points, and is denoted by l . The arity k 0 of l is arbitrary, but xed for every l. Let N ....

[Article contains additional citation context not shown here]

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [21], chapter 2, pages 95-162.

....( 2001 Published by Elsevier Science B. V. nested graphs are compositional since they forbid edges that cross component boundaries. Graph transfovnation is a rich theory for rule based computations on graphs [21] We combine simple concepts of graph transformation, like edge replacement [4] and substitutive transformation [19] to a new way of nested graph transformation that is based on variable matching and instantiation. We find this intuitive, elegant, and particularly useful for programming, as it resembles other rule based computational models, e.g. term rewriting [15] ....

.... lists, root connected trees and the like [23] Here we devise a means to specify shapes of graphs in a way that is not possible on the level of imperative languages (nor in functional or logical languages where pointers are hidden altogether) The specification is based on edge replacement [4], but we immediately adopt a terminology fitting to our purposes. Shape Grammars. The handle graph of a label l A consists of one straight k ary edge that is attached to k pairwise distinct points, and is denoted by l . The arity k 0 of l is arbitrary, but fixed for every l. Let N C A be ....

[Article contains additional citation context not shown here]

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [21], chapter 2, pages 95-162.

....the R dependent part. This part contains for every term rewrite rule (s t) 2 R exactly one net rewrite rule H(s t) This rule has the remarkable feature that it replaces only a single hyperedge. Such rules are called hyperedge replacement rules and are well studied in the literature (see [DHK] for an overview) Definition 8. Let G 2 AN (l;m) Gamma , H 2 AN Gamma The composition of G and H denoted by G ffi H 2 AN (l;n) Gamma , results from the disjoint union of G and H by gluing the nodes top(G) i and bottom(H) i for every 1 i m. Let g be the canonical injective embedding ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Transformations, Vol. I: Foundations, Chapter 2. World Scientific, to appear.

....graphs that are used for software modeling [3, 7] nested graphs are compositional since they forbid edges that cross component boundaries. Graph transformation is a rich theory for rule based computations on graphs [21] We combine simple concepts of graph transformation, like edge replacement [4] and substitutive transformation [19] to a new way of nested graph transformation that is based on variable matching and instantiation. We nd this intuitive, elegant, and particularly useful for programming, as it resembles other rule based computational models, e.g. term rewriting [15] ....

.... lists, root connected trees and the like [23] Here we devise a means to specify shapes of graphs in a way that is not possible on the level of imperative languages (nor in functional or logical languages where pointers are hidden altogether) The speci cation is based on edge replacement [4], but we immediately adopt a terminology tting to our purposes. 7 Shape Grammars. The handle graph of a label l 2 consists of one straight k ary l edge that is attached to k pairwise distinct points, and is denoted by l . The arity k 0 of l is arbitrary, but xed for every l. Let ....

[Article contains additional citation context not shown here]

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [21], chapter 2, pages 95-162.

....consists of just a single Flowchart edge. Again, conn edges, and now Conn edges, too, are grayed out since they are actually not required for free hand editing, but for syntax directed editing (cf. Section 4) Context free hypergraph grammars can describe only very limited hypergraph languages [12,14] and, therefore, are not suited for specifying the syntax of many diagram languages. 4 Context free hypergraph grammars with embeddings are more expressive than context free ones. They additionally allow 4 Actually, the only diagram languages that we know about and which can be described by ....

F. Drewes, A. Habel, H.-J. Kreowski, Hyperedge replacement graph grammars, in: Rozenberg [29], Ch. 2, pp. 95--162.

....that are used for software modeling [3, 9] sacrifice compositionality by allowing edges that cross component boundaries. Typing of values and operations is important for detecting inconsistencies in programs. We require that the shapes of graphs are specified by context free graph grammars [6], and refine transformation so that only shaped hierarchical graphs are manipulated. This goes beyond related typing concepts for graphs, which merely restrict the labelling and degree of nodes and edges [23] This paper is structured as follows: In sections 2 and 3 we recall substitutive ....

.... as doublylinked lists, root connected trees and the like [22] Here we devise a means to specify shapes in a way that is not possible on the level of imperative languages (nor in functional or logical languages where pointers are hidden altogether) The specification is based on edge replacement [6], but we immediately adopt a terminology fitting to our purposes. Shape Grammars. A shape rule s has the form n : R. It associates a shape name n 2 n X with a variable free pointed hierarchical graph R. The shape rule s directly derives a hierarchical graph G to a hierarchical graph H by ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [20], chapter 2, pages 95--162.

....MaxfCard( G) twd(G) 1g where twd(G) denotes the tree width of G. 47 A subset of HS(C) is called an HR set of hypergraphs i it is HS equational. The terminology HR refers to an equivalent characterization in terms of Hyperedge Replacement grammars studied in another chapter of this book ([29]) We give here the example of series parallel graphs. We shall use the source labels 1, 2, 3, and one edge label a of type 2. We de ne from the operations of FHR (f1; 2; 3g) the following operations : G= G 0 = G= C;C G 0 where C = f1; 2g and G; G 0 2 HS(C) G:G 0 = ren h (G= ....

....5.8 and 5.12 because the transduction f(j G j 2 ; j G j 1 ) G is a graphg is de nable (one can also say that the identity on simple directed graphs is (2; 1) de nable ; see Fact 4.3. 1) Implications (1) 2) and (1) 3) follow easily from general properties of HR sets of graphs (see chapter [29] in this book) The implications (2) 1) and (3) 1) are dicult : see Courcelle [19] 2 One can extend Theorem 5.15 as follows. A set L H(A) of simple hypergraphs (without sources) is said to be VR i it is the image of B under a ( 1) de nable transduction. Hence we use here the ....

: DREWES F., HABEL A., KREOWSKI H.-J., Hyperedge replacement graph grammars, this volume.

....complexity and allows for processing of diagram languages which could not be efficiently processed otherwise. Figure 2 shows two visualizations of an abstract control flow graph. Figure 3 shows how the syntax of abstract control flow graphs is specified, by context free graph transformation [4]. Diagrams can be manipulated in two ways: Free hand editing manipulates diagram components, and triggers re scanning and re parsing of the diagram; ff Omega Phi Psi x : 0 p s ff Omega Phi Psi P( p s ff Omega Phi Psi x = 1 p Gamma ff Omega Phi Psi x 0 ....

DREWES, F., HABEL, A., AND KREOWSKI, H.-J. Hyperedge replacement graph grammars. In Rozenberg [13], ch. 2, pp. 95--162.

....to describe even a useful approximation of a diagram language. The set of all class diagrams [33] for example, Engels et al. From Trees to Graphs 5 can not be generated by a hyper edge replacement graph grammar, because the number of edges in the graphs generated by such a grammar is bounded [14]. For this reason, visual language definitions often have to resort to non context free grammars (cf. 36, 31] As a consequence, the concept of derivation tree as representation of the process of constructing a sentence is no longer applicable. In fact, in order to record the history of a ....

DREWES, F., KREOWSKI, H.-J., AND HABEL, A. Hyperedge replacement graph grammars. In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, G. Rozenberg, Ed. World Scientific, 1997, pp. 95 -- 162.

....to Graph Transformation I: Basic Concepts and Double Pushout Approach [EHK 96] Ehrig, H. Heckel, R. Korff, M. Lowe, M. Ribeiro, L. Wagner, A. and Corradini, A. Algebraic Approaches to Graph Transformation II: Single Pushout Approach and Comparison with Double Pushout Approach [DKH96] Drewes, F. Kreowski, H. J. Habel, A. Hyperedge Replacement Graph Grammars [Sch96] Schurr, A. Programmed Graph Replacement Systems [EHR96] Ehrenfeucht, A. Harju, T. Rozenberg, G. 2 Structures, A Framework for Decomposition and Transformation of Graphs [Cou96a] Courcelle, B. The ....

F. Drewes, H.-J. Kreowski, and A. Habel. Hyperedge replacement graph grammars. In G. Rozenberg, editor, The Handbook of Graph Grammars, Volume 1: Foundations. World Scientific, 1996.

....languages is developed in detail. Among the most important topics are: context freeness, characterizations of HR languages, a pumping lemma for HR languages, generative power of HR grammars, predicates and numeric functions on hypergraphs compatible with the derivation process. The survey paper [DHK96] presents the concept of Hyperedge Replacement as one of the most elementary, best studied, and frequently used approaches to graph and hypergraph rewriting. In particular, HR grammars are discussed as a (hyper)graph grammatical counterpart to context free string grammars. To give a ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Handbook of Graph Transformations. Vol. I: Foundations (G.Rozenberg, ed.). World Scientific. To appear.

....aspects are context free grammars and transformations, called transductions in language theory. There are many types of context free graph grammars, some based on node replacement and others on (hyper)edge replacement. For the historical developments, see, e.g. Nag79, Nag80, ER96] and [Hab92a, DHK96] respectively. General requirements for a (graph) grammar to be called context free are formulated in [Cou87] the replacement mechanism should be confluent and associative. During the last ten years two main types of context free graph grammars have emerged: HR grammars, which are based on ....

....languages is developed in detail. Among the most important topics are: context freeness, characterizations of HR languages, a pumping lemma for HR languages, generative power of HR grammars, predicates and numerical functions on hypergraphs compatible with hyperedge replacement. The survey paper [DHK96] presents the concept of Hyperedge Replacement as one of the most elementary and best studied approaches to (hyper)graph rewriting. As a representative view of the theory of hyperedge replacement, structural properties, decision problems, and the membership problem are considered. For a tutorial ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Handbook of Graph Transformations. Vol. I: Foundations (G.Rozenberg, ed.). World Scientific. To appear.

....number of tentacles. The hyperedge label determines the number of tentacles. Each tentacle is connected to a node. Directed edges are hyperedges with a source and a target tentacle. This definition of hyperedge labeled hypergraphs over a certain label set corresponds to 0 hypergraphs defined in [31]. A visual sentence consists of a set of pictorial objects that are related in a way specific to the VL. Such objects are indivisible visual structures that are created, deleted, and related to other objects using editors in a VL environment. Hypergraphs offer a natural representation of visual ....

....d represent vertices of a rectangle. k is some constant value. of hypergraphs representing correct visual sentences. The simplest hypergraph grammar type is the class of context free hypergraph grammars which are quite similar to context free string grammars and which are discussed in detail in [31]. A context free hypergraph grammar has context free productions only. The LHS of each production consists of a single hyperedge labeled by a nonterminal symbol. The RHS consists of an arbitrary hypergraph over terminal and nonterminal symbols. Each node of the LHS has a corresponding node of the ....

[Article contains additional citation context not shown here]

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In [88], chapter 2, pages 95--162.

....them ) Fig. 1. Two transformation steps on list graphs 2 so that different relations, of any arity, can be represented in a single graph. We also distinguish a sequence of nodes as the points at which a graph may be connected to other graphs. Such graphs are known as pointed hypergraphs [6]. Usually, graphs are flat: Their nodes and edges are primitive; none of them may contain a nested graph. We, however, distinguish a subset of the edges in a graph H as frames: Every frame f contains a nested subgraph H f that may contain frames again. These graphs are called hierarchical in ....

....the variable L binds list graphs of type L , and the variable X binds graphs of the any type , and is instantiated by the type I of item graphs in the transformations of Example 2 and 4. 2 The rules used for shape definitions are a well studied special case of context free graph transformation [6]. Type checking thus amounts to context free graph parsing, as it is implemented in DIAGEN (see Section 6) Note that even if graph parsing may be expensive, it is done statically, before executing the program, and will also reduce the search space for graph matching at runtime. 8 L : 1 2 j ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [22], chapter 2, pages 95--162.

.... of the equational subsets of certain algebras of relational structures, with a binary gluing operation and all possible quantifier free first order definable unary operations, is presented in [Cou5] For a recent survey on C edNCE see [ER2] Other surveys that discuss work on C edNCE and HR are [Cou8, DHK, Eng5, Eng6]. For graph grammars in general see [Roz, ENRR, EKR, CEER] 2 Preliminaries N = f0; 1; 2; g and for m;n 2 N, m; n] fm; ng. The domain of a function f is denoted dom(f ) 2.1 Graphs, trees, and strings The reader is assumed to be familiar with formal language theory (see, e.g. ....

F.Drewes, A.Habel, H.-J.Kreowski; Hyperedge replacement graph grammars, Chapter in [Roz]

No context found.

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation. Vol. I: Foundations, chapter 2, pages 95--162. World Scientific, Singapore, 1997.

No context found.

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation. Vol. I: Foundations, chapter 2, pages 95--162. World Scientific, Singapore, 1997.

....EH are disjoint, for every graph H . Remark. In order to avoid confusion we remark that the hypergraphs used in the short version of this paper [14] come with an additional component, namely a sequence of distinguished nodes called points. These are useful in connection with hyperedge replacement [13], which is employed by the attening process considered in Section 6. However, as long as one is not interested in attening, and in particular as far as the basic theory is concerned, points are of no particular value they just complicate the whole theory in an unnecessary way. This is the reason ....

....G ) t , where G , H , and t are the attened versions of G, H , and t, respectively. Obviously, the converse cannot hold as structural information gets lost in the attening process. For the de nition of attening, we extend the well known concept of hyperedge replacement (see [25, 13]) to hierarchical graphs. Let H be a hierarchical graph. For every set E EH of edges, H E denotes the hierarchical graph obtained by deleting all the edges in E from H , i.e. H E = hG; FH n E; ctsi where G = hVH ; EH nE; att ; labi, att and lab being the restrictions of att H and lab H to EH ....

Frank Drewes, Annegret Habel, and Hans-Jorg Kreowski. Hyperedge replacement graph grammars. In Rozenberg [40], chapter 2, pages 95-162.

....loop. In this example, is the only nonterminal. We write : R 1 j jRn to abbreviate several rules : R 1 ; Rn for the same nonterminal. Syntactic rules specify hyperedge replacement, which derives one of the beststudied classes of context free graph languages (see [11, 4] for details) Such rules allow to de ne recursive algebraic data types of functional and logical languages, and sophisticated pointer structures like cyclic lists, or leaf connected trees, which cannot be de ned in imperative languages (see also [10] Membership in these languages is ....

....recursively, the subterm t i . In this case, plain graph matching can be done in constant time and thus occurrences can be found eciently. In more general cases, one can make use of algorithms which compute the set of all derivation trees of G(v) with respect to the shape grammar; see [4] for a discussion of derivation trees) If this can be done in polynomial time, matchings can usually be found in polynomial time as well. This is because P is also shaped, and hence each P (u) can be represented by its set of derivation trees. The latter can be matched against the derivation ....

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [21], chapter 2, pages 95-162.

....disjoint, for every graph H . Remark. In order to avoid confusion we remark that the hypergraphs used in the short version of this paper [DHP00] come with an additional component, namely a sequence of distinguished nodes called points. These are useful in connection with hyperedge replacement [DHK97] which is employed by the attening process considered in Section 7. However, as long as one is not interested in attening, and in particular as far as the basic theory is concerned, points are of no particular value they just complicate the whole theory in an unnecessary way. This is the ....

....0 , where G 0 , H 0 , and t 0 are the attened versions of G, H , and t, respectively. Obviously, the converse cannot hold as structural information gets lost in the attening process. For the de nition of attening, we extend the well known concept of hyperedge replacement (see [Hab92, DHK97] to hierarchical graphs. Let H be a hierarchical graph. For every set E EH of edges, H E denotes the hierarchical graph obtained by deleting all the edges in E from H , i.e. H E = hG; FH n E; ctsi where G = hV H ; EH n E; att ; labi, att and lab being the restrictions of att H and lab H to EH ....

Frank Drewes, Annegret Habel, and Hans-Jorg Kreowski. Hyperedge replacement graph grammars. In Rozenberg [Roz97], chapter 2, pages 95-162.

No context found.

DREWES, F., KREOWSKI, H.-J., AND HABEL, A. Hyperedge replacement graph grammars. In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, G. Rozenberg, Ed. World Scientic, 1997, pp. 95 -- 162.

No context found.

F. Drewes, A. Habel, and H. Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation. Vol. I: Foundations, chapter 2, pages 95--162. World Scientific, 1997.

No context found.

F. Drewes, H.J. Kreowski, and A. Habel. Hyperedge replacement graph grammars. In G. Rozemberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation: Foundations, volume 1, chapter 2, pages 95--162. World Scientific, 1997.

No context found.

F. Drewes, A. Habel, and H.-J. Kreowski. Hyperedge replacement graph grammars. In Rozenberg [20], chapter 2, pages 95-162.

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