H. Ehrig, H.-J. Kreowski, and G. Taentzer, Canonical Derivations in High-Level Replacement Systems, Tech. Report 6/92, University of Bremen, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... HLR0 [EHKP91] local Church Rosser Theorem I,II HLR1 [EHKP91] Parallelism Theorem without bijective correspondence HLR1 [EHKP91] with bijective correspondence HLR1 [EHKP91] Canonical Dependency Relation HLR2 [EHKP91] Concurrency Theorem HLR2 [EHKP91] Existence of Canonical Derivations HLR1 [EKT92] Uniqueness of Canonical Derivations HLR1 [EKT92] Static Parallel Derivation Theorem HLRP [ET92] Tae92] Dynamic Parallel Derivation Theorem HLRP [ET92] Tae92] Embedding Theorem I HLR1 [PT93] Embedding Theorem II HLR2 [PT93] Embedding Theorem III HLR2 and HLRI [PT93] Distributed ....

.... [EHKP91] Parallelism Theorem without bijective correspondence HLR1 [EHKP91] with bijective correspondence HLR1 [EHKP91] Canonical Dependency Relation HLR2 [EHKP91] Concurrency Theorem HLR2 [EHKP91] Existence of Canonical Derivations HLR1 [EKT92] Uniqueness of Canonical Derivations HLR1 [EKT92] Static Parallel Derivation Theorem HLRP [ET92] Tae92] Dynamic Parallel Derivation Theorem HLRP [ET92] Tae92] Embedding Theorem I HLR1 [PT93] Embedding Theorem II HLR2 [PT93] Embedding Theorem III HLR2 and HLRI [PT93] Distributed Derivations HLR1 [Pad92] PER93] Fusion HLR1.5 ....

H. Ehrig, H.-J. Kreowski, and G. Taentzer, Canonical Derivations in High-Level Replacement Systems, Tech. Report 6/92, University of Bremen, 1992.

....a specific category of graphs; one whose objects have coloured nodes and coloured edges, with source and target functions mapping each edge to its source and target. However the underlying algebraic construction is very general and can be adapted to many other categories of graph like systems (see Ehrig et al. 1991a,b, 1993)) Since the main point that this paper makes is algebraic in nature, it too can be adapted to many such categories. However, rather than seek the greatest possible generality in the presentation, by heavy use of universal algebra, we will pick a fairly simple category of graphs to work with, and ....

Ehrig H., Kreowski H-J., Taentzer G. (1993); Canonical Derivations for High-Level Replacement Systems, in: Graph Transformations in Computer Science, Schneider, Ehrig (eds.), Lecture Notes in Computer Science 776, 152-169, Springer, Berlin.

....in cooperation with F. Parisi Presicce (Rome) in order to unify DPO approaches based on different kinds of graphs and structures [EHKP92] In the second phase theory and applications of HLR systems were extended in various ways, especially to include canonical derivation sequences in the theory [EKT94] and transformations of algebraic specifications and algebraic high level nets in the applications. Moreover, the HLR approach was extended to the SPO approach in the second phase [EL93a] An interesting notion of categorical graph grammars was developed by H. J. Schneider (Erlangen) Sch93] 4 ....

....are the graph grammatical counterpart to leftmost derivations in Chomsky grammars. Within COMPUGRAPH II the groups in Berlin and Bremen were able to generalize this result to HLR systems (2. 2) including graphs, hypergraphs, structures, algebraic specifications and algebraic high level nets [EKT94] Moreover, H. J. Kreowski has presented an axiomatic approach to canonical derivation sequences [Kre94] Parallel and Distributed Graph Grammars and Synchronization Mechanisms Parallel and distributed graph grammars have been developed in the algebraic approach already in the 70 s and 80 s. ....

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H. Ehrig, H-J. Kreowski, and G. Taentzer. Canonical derivations for high level replacement systems. In Lecture Notes in Computer Science 776, pages 153--169. Springer Verlag, 1994. Also Technical Report 6/92, University of Bremen.

.... Using HLR systems one can clarify the relationship between several choices of specification morphisms in algebraic specifications from the rewriting point of view [EP91b] The theory of HLR systems (based on the DPO approach) was further extended to include also canonical derivation sequences [EKT94] parallel graph grammars [ET92, Tae96] and embeddings of derivations [PT95] New applications of HLR systems to transformations of Petri nets and algebraic specifications have been studied in [PER95] and [EP93] Based on HLR systems, rule based refinement, its abstract relation to other kinds ....

....derivations in Chomsky grammars. As such, they can be regarded as standard representatives 17 for equivalence classes of derivations with respect to the so called shift equivalence . Such an equivalence relates derivations which apply non causally related derivation steps in any order. In [EKT94] Ehrig, Kreowski and Taentzer generalize canonical derivations, previously studied for string and graph grammars only, from graph grammars to high level replacement systems, short HLR systems. It turns out that basic results concerning synthesis and analysis of parallel derivation sequences in ....

H. Ehrig, H.-J. Kreowski, and G. Taentzer. Canonical derivations for high level replacement systems. In Lecture Notes in Computer Science 776, pages 153--169. Springer Verlag, 1994. Also Technical Report 6/92, University of Bremen.

....of the objects that are rewritten. Therefore the large body of results and constructions of the algebraic approaches can be extended quite easily to cover the rewriting of arbitrary structures (satisfying certain properties) as shown for example by the theory of High Level Replacement Systems [22,23]. In this section, we first introduce informally the basic notions of graph, production and derivation for the DPO and SPO approaches in Section 2.1. We address questions concerning the independence of direct derivations and their parallel application in Section 2.2; the embedding of derivations ....

....k 2 = y ffi k 2 , because (7) is a pushout. ffl Since (7) and (7) 8) are pushouts, also (8) is a pushout. Thus q is injective because so is u. Square (8) is also a pullback because all its morphisms are injective. ffl Finally, by the so called pushout pullback decomposition property (see [22]) which holds for category Graph (with injective morphism as distinguished class of morphisms M) since (6) 8) is a pushout, 8) is a pullback, and morphisms r 1 , u, v, q and p are injective, then (6) is a pushout as well. ut The next easy technical lemma will be helpful in the proof of the ....

H. Ehrig, H.-J. Kreowski, and G. Taentzer. Canonical derivations for high-level replacement systems. In H.-J. Schneider and H. Ehrig, editors, Proceedings of the Dagstuhl Seminar 9301 on Graph Transformations in Computer Science, volume 776 of Lecture Notes in Computer Science, pages 153--169. Springer Verlag, 1994.

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