Advertisement

Decomposition of graph grammar productions and derivations

  • Hartmut Ehrig
  • Barry K. Rosen
List Of Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 73)

Abstract

Given a production p* in a graph grammar we consider the problem to find all productions p and p′ and all dependency relations R between p and p′ such that p* is equal to the concurrent production p*Rp′. In view of the Concurrency Theorem — shown in an earlier paper — this means that there is a bijective correspondence between direct derivations G⇒ X via p* and R-related derivations G⇒ H⇒ X via (p,p′). We are able to give a general procedure for the decomposition of p*=p*Rp′ which leads to all possible decompositions at least in the case of injective relations R. An important application of this decomposition theorem is the problem to find all possible decompositions of manipulation rules into atomic manipulation rules of a data base system. The theorem is proved within the framework of the algebraic theory of graph grammars using pushout and pullback techniques.

Key Words

Decomposition Graph Grammars Concurrency Applications of Category Theory to Graph Grammars 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5. References

  1. /AM 75/.
    Arbib, M.A.; Manes, E.G.: Arrows, Structures and Functors: The Categorical Imperative, Academic Press, New York, 1975Google Scholar
  2. /BA 78/.
    Batini, C.; D'Atri, A.: Rewriting Systems as a Tool for Relational Data Base Design, Proc. International Workshop on Graph Grammars and Their Applications to Computer Science and Biology, Bad Honnef 1978, this volumeGoogle Scholar
  3. /Eh 78/.
    Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars, Proc. International Workshop on Graph Grammars and Their Applications to Computer Science and Biology, Bad Honnef 1978, this volumeGoogle Scholar
  4. /EK 76/.
    Ehrig, H.; Kreowski, H.-J.: Contributions to the Algebraic Theory of Graph Grammars, Techn. Report 76-22, FB 20, TU Berlin (1976), to appear in Math. Nachr.Google Scholar
  5. /EK 78/.
    —: Algebraic Theory of Graph Grammars Applied to Consistency and Synchronization in Data Bases, Proc. Workshop WG 78 on Graphtheoretic Concepts in Computer Science, to appear in the series Applied Computer Sci.Google Scholar
  6. /ER 78/.
    Ehrig, H.; Rosen, B.K.: Concurrency of Manipulations in Multidimensional Information Structures, Techn. Rep. 78-13, FB 20, TU Berlin (1978), short version in Proc. MFCS'78, Springer Lect. Notes Comp. Sci (64), 165–176 (1978)Google Scholar
  7. /Fu 78/.
    Furtado, A.L.: Transformations of Data Base Structures, Proc. International Workshop on Graph Grammars and Their Applications to Computer Science and Biology, Bad Honnef 1978, this volumeGoogle Scholar
  8. /Ne 77/.
    Negraszus-Patan, G.: Anwendungen der algebraischen Graphentheorie auf die formale Beschreibung und Manipulation eines Datenbankmodells, Diplomarbeit, FB 20, TU Berlin (1977)Google Scholar
  9. /St 78/.
    Steiner, S.: Untersuchungen über die gleichzeitige Ausführung von Operationen in Datenbankmodellen unter Verwendung der Algebraischen Graphentheorie, Diplomarbeit FB 20, TU Berlin (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Hartmut Ehrig
    • 1
  • Barry K. Rosen
    • 2
  1. 1.Fachbereich Informatik TechnUniversität BerlinBerlin 10Germany
  2. 2.Computer Science Dept.IBM Research CenterYorktown HeightsUSA

Personalised recommendations