A.Habel; Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992  Home/Search   Document Not in Database   Summary   Related Articles   Check

....languages generated by HR grammars. 1 Introduction Context free graph languages are generated by context free graph grammars, which are usually graph replacement systems. One of the most popular types of context free graph grammar is the Hyperedge Replacement System, or HR grammar (see, e.g. [Hab, HabKre, HabKV]) A completely di#erent way of generating graphs is to select a number of graph operations, to generate a set of expressions (built from these operations) and to interpret the expressions as graphs. The set of expressions is generated by a classical context free grammar generating strings (or ....

....interpreted as graph languages. Note that an interpretation looks like a semi group homomorphism; however, it is not exactly one, because concatenation on graphs is, in fact, a partial operation. More precisely, graphs are typed, and concatenation is defined only if the types fit . In fact, as in [Hab], our graphs are equipped with a designated sequence of begin nodes and a designated sequence of end nodes (generalizing the idea that strings have a beginning and an end) A graph g 1 can be concatenated with a graph g 2 only if the sequence of end nodes of g 1 has the same length as the ....

[Article contains additional citation context not shown here]

A.Habel; Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992

....Slissenko on his 60th birthday 1 Introduction and main results To honor A. Slissenko s 60th birthday we deal with a topic related to A. Slissenko s work [Sli79,Sli82] 3 . In [Sli82] Slissenko showed that on classes K of graphs generated by certain graph grammars, called Slissenko grammars in [Hab92] the existence of Hamiltonian cycles (HAM) can be decided in polynomial time. Under suitable coding of graphs 4 as with vertices and edges as universes, HAM is definable in Monadic Second Order Logic (MSOL) We look for necessary and sufficient conditions on a class K of (possibly colored) ....

Annegret Habel. Hyperedge Replacement: Grammars and Languages. Lecture Notes in Computer Science, Vol. 643. Springer-Verlag, Berlin, 1992.

.... computed by first creating the colimes of all match morphisms of the di#erent patterns into the hypergraph model together with all these morphisms P # P # R, and then removing the edges and unnecessary nodes of the hypergraph model from the colimes hypergraph [10] 12 graph grammar (e.g. [12]) which generalizes the idea of Chomsky grammars for strings which are also used by standard compiler generators [13] Because of the similarity of diagram analysis with program analysis being performed by compilers and the availability of derivation trees and directed acyclic graphs (DAGs, see ....

....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 ....

A. Habel, Hyperedge Replacement: Grammars and Languages, Vol. 643 of Lecture Notes in Computer Science, Springer, 1992.

....proving properties of such graph generating tree grammars. 1 Introduction The most well known way of generating graphs is to replace a subgraph by another subgraph, analogous to string rewriting systems. The resulting theory of graph grammars has been developed since the seventies (see, e.g. [41, 20, 19, 32, 7]) Of particular interest are the context free graph grammars, in which the replaced subgraph is a single edge or node. Such grammars model graph properties that can be defined in a recursive way. A conceptually completely different way of generating graphs is to use symbolic computation, as ....

....graph languages (see [9, 12, 14] The equivalence of HR with these sets of operations will be shown in Proposition 8. Thus, they all define the HR context free graph languages. It was proved in [1] that these are exactly the graph languages generated by the Hyperedge Replacement graph grammars of [33, 32, 18, 1]. The set of operations VR was defined in [15] To be precise, it was defined for a more general type of graphs (in which one node can have several port labels) the equivalence of the two sets of operations was shown in Lemma 1.1 of [8] using a tree transducer and applying Proposition A, as in ....

[Article contains additional citation context not shown here]

A.Habel; Hyperedge replacement: grammars and languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992

....results derived using a hyper edge replacement graph grammar approach. Hence the title of this thesis: Graphs Grammars and Operations on Graphs . In what follows, we will make comparisons to work of Engelfriet and Heyker ( EH91] EH92] Bauderon and Courcelle ( BC87] and Habel and Kreowski ([Hab92]) all of which are hyper edge replacement oriented approaches. No comparison whatsoever is made with node replacement oriented approaches. It may be interesting to observe that node replacement is in general more powerful than edge replacement. For example, the set of all complete graphs can ....

....and Heyker in 1992, see [EH92, page 171] 11.9 Further reading As noted, for an overview of recent developments in the field of graph grammars, ENRR87] and [EKR91] are a good place to start, especially because they contain comprehensive tutorials. Furthermore, the Ph.D. thesis of Habel [Hab92] contains lots of interesting results. As a matter of fact, at the time of this writing it is the only existing book on the (modern) theory of context free graph grammars, and one of the few books at all, and probably the most up to date one, on graph grammars. Finally, the reader should be well ....

Annegret Habel, Hyperedge replacement: grammars and languages, Lecture Notes in Computer Science, vol. 643, Springer-Verlag, Berlin, 1992, ISBN 3540 -56005-X (originally appeared as Ph.D. thesis, Bremen).

....types of hypergraph grammars, such as node replacement grammars and hyperedge replacement grammars. Especially hyperedge replacement grammars have nice context free properties. When analyzing hypergraphs it is important to determine the values of some numerical functions on these hypergraphs. In [Hab92], a large number of numerical functions on hypergraphs is presented. It is shown that the boundedness of the values of these functions on hypergraph languages, which are generated by hyperedge replacement grammars, is decidable if the functions are compatible with the replacement of hyperedges by ....

....expressions. Evaluating these numerical expressions yields the function values. We will show that for a special class of sets of hypergraph expressions, called regular (hypergraph) expression languages, generated by regular expression grammars, we can obtain similar decidability results as in [Hab92]. In Chapter 2, all the mathematical notions and notations used in this thesis are presented. In Chapter 3, tree grammars and automata are treated. Since expressions closely correspond to trees, these devices are relevant for the above approach. The regular tree grammars are presented, as are tree ....

[Article contains additional citation context not shown here]

Annegret Habel, Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science, Vol. 643, Springer Verlag, Berlin, Germany, July 1992.

....and recursive families of graphs In this section, we consider some types of graph grammars, the recursive families of graphs and their relationships to treewidth. We will limit the presentation here to a few notions and results, and direct the readers for further reading to other sources, e.g. [30, 36, 46, 45]. 8.1 Hyperedge replacement grammars First, we consider the notion of hyperedge replacement grammar, introduced by Habel and Kreowski. We only give an informal description here: for a good introduction to this topic, see e.g. 45, 46] The framework of context free graph grammars of Bauderon ....

....readers for further reading to other sources, e.g. 30, 36, 46, 45] 8.1 Hyperedge replacement grammars First, we consider the notion of hyperedge replacement grammar, introduced by Habel and Kreowski. We only give an informal description here: for a good introduction to this topic, see e.g. [45, 46]. The framework of context free graph grammars of Bauderon and Courcelle is essentially similar [8] See also [66] Hyperedge replacement grammars work with hypergraphs, where each hyperedge is represented as a sequence of vertices. A hyperedge also has a label, which is either a terminal label, ....

A. Habel, Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science, Vol. 643, Springer-Verlag, Berlin, 1992.

....given of the largest class K # such that Int(K # ) Int(K) Context free graph languages are generated by context free graph grammars, which are graph replacement systems. One of the most popular types of context free graph grammar is the Hyperedge Replacement System, or HR grammar (see, e.g. [9]) A completely different way of generating graphs (introduced in [1] is to select a number of graph operations, to generate a set of expressions (built from these operations) and to interpret the expressions as graphs. The set of expressions is generated by a classical context free grammar ....

....(as defined in [1] and all constant graphs, a collection of graph operations is obtained that is simpler than the one in [1] but also has the power of the HR grammar (which is our first result) Let us be a bit more precise. We consider the multi pointed graphs (or multi pointed hypergraphs) of [9]. For simplicity we will restrict ourselves in this paper to graphs, but all arguments also hold for hypergraphs. A multi pointed graph is a directed, edgelabeled graph g with a designated sequence begin(g) of begin nodes and a designated sequence end(g) of end nodes . If begin(g) has length ....

A. Habel; Hyperedge replacement: grammars and languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992.

....languages generated by HR grammars. 1 Introduction Context free graph languages are generated by context free graph grammars, which are usually graph replacement systems. One of the most popular types of context free graph grammar is the Hyperedge Replacement System, or HR grammar (see, e.g. [Hab, HabKre, HabKV]) A completely different way of generating graphs is to select a number of graph operations, to generate a set of expressions (built from these operations) and to interpret the expressions as graphs. The set of expressions is generated by a classical context free grammar generating strings (or ....

....interpreted as graph languages. Note that an interpretation looks like a semi group homomorphism; however, it is not exactly one, because concatenation on graphs is, in fact, a partial operation. More precisely, graphs are typed, and concatenation is defined only if the types fit . In fact, as in [Hab], our graphs are equipped with a designated sequence of begin nodes and a designated sequence of end nodes (generalizing the idea that strings have a beginning and an end) A graph g 1 can be concatenated with a graph g 2 only if the sequence of end nodes of g 1 has the same length as the ....

[Article contains additional citation context not shown here]

A.Habel; Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992

....one nonterminal node. It is easy to see that LIN edNCE B edNCE. It is shown in [EL1] that A edNCE and LIN edNCE are incomparable subclasses of B edNCE. The class B edNCE also contains the B NLC languages of [RW] and (as shown, e.g. in [ER1] the hyperedge replacement (HR) graph languages of [BC, HK, Hab]. Grammar G 1 from Example 1 is both linear and apex. Grammar G 0 2 is boundary, but not linear or apex. Grammars G 2 and G 3 are not boundary. The class A edNCE can be characterized within the class C edNCE: there is a simple condition on a graph language L 2 C edNCE that expresses membership ....

....type of) graph language. For a class of graph languages K, we denote by STR(K) the class of all string languages in K. The string languages generated by graph grammars in this way were investigated in [EH1] for another type of context free graph grammars: the hyperedge replacement grammars of [Hab]. However, it is known that these grammars have the same string generating power (in this sense) as the C edNCE grammars (see, e.g. Bra3, EH2] From this we find that STR(C edNCE) OUT(DTWT) the output languages of deterministic tree walking transducers, and STR(LIN edNCE) OUT(2DGSM) the ....

A.Habel; Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, 1992

....one perceives a graph as a set of edges which are joined at their end points, i.e. nodes, permitting an arbitrary number of nodes incident to a (hyper)edge is a natural extension. It leads to the notion of hypergraphs and the concept of hyperedge rewriting, the theory of which is developed in [6]. Other techniques of hypergraph rewriting are in particular the handle rewriting approaches in [4] and [9] As a first step towards integrating node and hyperedge rewriting, node rewriting in graphs is adapted to hypergraphs in [10] by generalising the NCE mechanism from edges to hyperedges. ....

....stay in Bordeaux. in graphs is translated into terms of pullback rewriting. A notion of node rewriting in hypergraphs with the pullback approach is presented in [3] The coding of hypergraphs used there is, however, not rich enough to capture hyperedges with an ordered set of tentacles as in [6] or [10] An application of pullback rewriting in hypergraphs to describe refinement in Petri nets is investigated in [11] The groundwork for a general theory of pullback rewriting is laid in [1] The aim of this paper is to translate the approach of NCE node rewriting in directed hypergraphs ....

[Article contains additional citation context not shown here]

Annegret Habel. Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643. Springer-Verlag, 1992.

....SEM. This should do no harm because it is always clear from the context which is which. All the graph grammar and graph rewrite approaches one encounters in the literature provide notions of graphs and rules and a way of directly deriving a graph from a graph by applying a rule (cf. e.g. [Ehr79, Nag79, JR80, Cou90, KR90, Sch91b, Him91, Hab92, Low93]) Therefore, all of them can be considered as graph transformation approaches in the above sense, if one chooses the components E and C in some standard way. The singleton set fallg with SEM(all) G may provide the only graph class expression, and the class of elementary control conditions may ....

A. Habel. Hyperedge replacement: Grammars and languages. Lecture Notes in Computer Science 643, 1992.

....is enigmatic and should be discussed each time separately. For example, the laws of physics nowadays are supposed to be local. Programming in computer science also prefers local conditions and local cycles. There were recent activity in graph grammars in computer science framework, see [4] and proceedings of four conferences in graph grammars, the first one is [5] Note however that graph grammars (more exactly, operations on spin graphs) appeared under another name earlier (see [10] One should realize there exist (and this is quite inevitable) a lot of different variations on ....

....grammars (more exactly, operations on spin graphs) appeared under another name earlier (see [10] One should realize there exist (and this is quite inevitable) a lot of different variations on the theme of graph grammars. All of them use different generalizations of spin graphs (see for example, [4] , 5] Examples are bipartite graphs (used in Petri nets) hypergraphs with hyperedges instead of edges. Choice of a particular definition depends on local historical tradition, personal taste and favourite applications. Most general framework for all these notions seems to be the category ....

A. Habel. Hyperedge Replacement: Grammars and Languages. Lecture Notes in Computer Science, v. 643, 1992. Springer Verlag.

.... which was first investigated in, e.g. Kau, Bra, Schu, Oos, Eng2] One advantage of the class C edNCE is that it is the largest known class of context free graph languages (where context free is taken in the sense of [Cou1] It includes, e.g. the HR (i.e. Hyperedge Replacement) languages of [BC, HK, Hab], the B NLC languages of [RW1, RW2] and the B edNCE languages of [ELW, EL] Thus, results on C edNCE apply to a quite large class of recursive praph properties. A second advantage of C edNCE is that it seems to be robust in the sense that it can be characterized in several different ways. It is ....

A.Habel; Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, 1992

....languages, specification of database systems, specification of abstract data types, specification of distributed systems, etc. This development is documented in proceedings and other collections of selected papers, in some monographs as well as in a handbook [CER79, ENR83, ENRR87, EKR91, Hab92, PvE93, SPvE93, SE94, CM95, CEER96, Roz97] This paper surveys some recent developments in applying graph transformation to the specification and development of systems, languages, and tools. Section 2 recalls the basic concepts of a fairly general approach to graph transformation, and points out ....

.... exist a variety of graph transformation approaches like Progres [SWZ95] algebraic ones like the double pushout approach [Ehr79] the single pushout approach [Low93] or Agg [TB94] and more restricted approaches like node replacement [JR80] edge replacement [HK87] or hyperedge replacement [Hab92] See for an overview [Roz97] They differ mainly in the underlying graph data model and the type of transformation rules. For example, in Progres attributed graphs are transformed, whereas Agg manipulates hierarchical ones with single pushout rules, and hyperedge replacement applies so called ....

Annegret Habel. Hyperedge Replacement: Grammars and Languages. Lecture Notes in Computer Science 643. Springer-Verlag, 1992.

....functional programming languages, specification of database systems, specification of abstract data types, specification of distributed systems, etc. This development is documented in proceedings and other collections of selected papers as well as in some monographs [CER79, ENR83, ENRR87, EKR91, Hab92, PvE93, SPvE93, SE94, CM95, CEER96] This paper surveys some recent developments in applying graph transformation to the specification and development of systems, languages, and tools. Section 2 recalls the basic concepts of a fairly general approach to graph transformation, and points out ....

.... to be widely applicable, Grace is intended to offer a variety of graph transformation approaches including a Progres like approach [Sch90, Sch91b] the algebraic ones [Ehr79, Low93] and more restricted approaches like node replacement [JR80] edge replacement [HK87] or hyperedge replacement [Hab92] Finally, it shall be possible to introduce new user defined approaches. Operational semantics. The operational semantics of a graph transformation system is usually defined as the set of all derivations. By abstracting from the intermediate steps of a derivation, one obtains an input output ....

Annegret Habel. Hyperedge Replacement: Grammars and Languages. Lecture Notes in Computer Science 643. Springer-Verlag, Berlin, 1992.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC