Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Theory of Computing Systems, 32:159-208, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....yields a generalization of known decidability results concerning boundedness problems for functions on graphs and other domains. The functions that can be dealt with are definable by recursion on the derivation tree of a graph. This does not require a particular 9 notion of graph rewriting. In [Dre98, Dre97] the structure of hyperedge replacement graph languages consisting of (hyper)trees is investigated. It is shown that these languages can be generated by productions whose right hand sides are themselves hypertrees. However, for this one has to turn to sets of derivation trees produced by a ....

Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Theory of Computing Systems, 1998. To appear.

....provides the use of already existing analysis techniques in the field of temporal logic. Furthermore, the construction of a minimal model is introduced allowing for the use of model checking. The contents of the following papers have been described in the First Annual Progress Report: Dre98a, DE98, Plu98] 4.1.4 Language Design Why not combining two successful principles in one formalism: rules and graphs This is the common vision of the graph transformation community and the main motivation behind the development of PROGRES, a visual language that supports PROgramming with Graph ....

Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Theory of Computing Systems, 32:159--208, 1998.

....languages which can be generated by context free graph grammars (which turns out to be the same for HR and NR) By our results this is the class of output languages of sur (or, equivalently, finite copying) MTTs taking regular tree languages as input. A related result has recently been proved in [Dre97]. In fact, the results of [Dre97] can be used to obtain, in a more direct way, the above characterization by MTTs of the tree languages generated by context free graph grammars, as shown in [EM] This paper is structured as follows. Section 2 contains basic notions concerning trees, tree ....

....by context free graph grammars (which turns out to be the same for HR and NR) By our results this is the class of output languages of sur (or, equivalently, finite copying) MTTs taking regular tree languages as input. A related result has recently been proved in [Dre97] In fact, the results of [Dre97] can be used to obtain, in a more direct way, the above characterization by MTTs of the tree languages generated by context free graph grammars, as shown in [EM] This paper is structured as follows. Section 2 contains basic notions concerning trees, tree translations, and tree languages. In ....

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F. Drewes. A characterization of the sets of hypertrees generated by hyperedgereplacement graph grammars. Technical Report Bericht Nr. 3/97, Universitat Bremen, 1997. (to appear in Theory of Comput. Sys.).

....tree transducer and the context free tree grammar [EV85, FV98] The class of tree languages obtained by unfolding the term graph languages which can be generated by HR grammars, is characterized in [EH92] as the class of output tree languages of attribute grammars. More recently it was proved in [Dre97] that TR(HR) can be obtained by evaluating the output tree languages of finite copying top down tree transducers [ERS80] in an algebra of hypergraphs in which each operation is a substitution into a tree graph. We show that the evaluation in such an algebra corresponds to a very restricted kind of ....

....of M 0 are precisely those of M , and that for q 2 Q and s 2 T Sigma , M 00 q (M 0 q (s) M q (s) Hence M 0 2 T fc and M = M 00 ffi M 0 . By a straightforward product construction. ut 4 Tree Graph Operations To state the characterization of TR(HR) by Drewes in [Dre97], we have to recall the characterization of HR in terms of operations on hypergraphs (cf. BC87, Eng94, Dre96] A hypergraph that contains variables z 1 ; z k can be seen as a k ary operation on hypergraphs. Let Z k = fz j i j 1 i k; j 0g with rank(z j i ) j. If g 2 HGR( Delta [ Z ....

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F. Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Technical Report Bericht Nr. 3/97, Universitat Bremen, 1997. (to appear in Theory of Comput. Sys.).

....Group APPLIGRAPH through the University of Bremen. 1 The idea to associate a tree grammar or tree transducer with an algebra that maps trees into a semantic domain was already mentioned in [14] For graphs generated by node or hyperedge replacement this has been worked out in [15] see also [3, 11, 9]) For the field of picture generation the idea seems to be new, however. In the main part of the paper four of the well known classes of picture generating devices found in the literature, namely collage grammars [22] mutually recursive function systems (a generalised type of iterated function ....

Frank Drewes. A characterization of the sets of hypertrees generated by hyperedgereplacement graph grammars. Theory of Computing Systems, 32:159--208, 1998.

....that otherwise would have to be derived independently. Top down tree transducers with the finite copying property can be used to achieve a similar effect by copying an input term (or a subterm thereof) and using the identical copies to synchronize sub derivations. This paper is a short version of [Dre97]. Due to the limitation of space, proofs are omitted or only sketched; details can be found in [Dre97] 2 Tree transductions For n 2 N, n] denotes the set f1; ng. The set of all finite sequences over a set S is denoted by S . For l 2 S , l] denotes the smallest subset S 0 of S ....

....property can be used to achieve a similar effect by copying an input term (or a subterm thereof) and using the identical copies to synchronize sub derivations. This paper is a short version of [Dre97] Due to the limitation of space, proofs are omitted or only sketched; details can be found in [Dre97]. 2 Tree transductions For n 2 N, n] denotes the set f1; ng. The set of all finite sequences over a set S is denoted by S . For l 2 S , l] denotes the smallest subset S 0 of S with l 2 S 0 . The length of l is denoted by jlj, and l(i) denotes the ith element of l. If f : A ....

Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Report 3/97, Univ. Bremen, 1997.

....with every derivation tree the corresponding picture. The idea to associate a tree grammar or tree transducer with an algebra that maps trees into a semantic domain was already mentioned in [Eng80] For graphs generated by node or hyperedge replacement this has been worked out in [Eng94] see also [CE95, DE96, Dre97]) For the field of picture generation the idea seems to be new, however. In the main part of the paper four of the well known classes of picture generating devices found in the literature, namely collage grammars [HK91] mutually recursive function systems (or hierarchical iterated function ....

Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Report 3/97, Univ. Bremen, 1997. Revised version to appear in Theory of Computing Systems.

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Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Theory of Computing Systems, 32:159-208, 1998.

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