Advertisement

Transformations of derivation sequences in graph grammars

  • Hans-Jörg Kreowski
Section B Computation Theory in Category
Part of the Lecture Notes in Computer Science book series (LNCS, volume 56)

Abstract

Basing on the Church-Rosser Theorems in /EK 76b/ analysis and synthesis of parallel derivations in graph grammars are introduced. This allows specific, transparent transformations of derivation sequences, which can be used as elementary steps of algorithms acting on derivations, and the calculation rules for transformations presented in this paper are needed to prove the correctness of such algorithms. One example of this kind is given: the equivalence of derivations in graph grammars is defined and canonical derivations representing the equivalence classes are specified. For graph grammars canonical derivations will be as important as leftmost derivations and respective concepts for classical Chomsky grammars to the design of correct parsing algorithms.

Keywords

Direct Derivation Graph Grammar Calculation Rule Derivation Sequence Shift Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. /Eh 77/.
    Ehrig, H.: Embedding Theorems in the Algebraic Theory of Graph Grammars, this volumeGoogle Scholar
  2. /EK 76a/.
    Ehrig, H., Kreowski, H.-J.: Categorical Approach to Graphic Systems and Graph Grammars, Conf. Report Algebraic System Theory, Udine 1975, Springer Lect. Notes in Econ. Math. Syst. 131 (1976), 323–351Google Scholar
  3. /EK 76b/.
    Ehrig, H., Kreowski, H.-J.: Parallelism of Manipulations in Multidimensional Information Structures, Proc. Conf. Math. Foundations of Comp. Sci., Gdańsk 1976, Springer Lect. Notes in Comp. Sci. 45 (1976), 284–293Google Scholar
  4. /EPS 73/.
    Ehrig, H., Pfender, M., Schneider, H.J.: GRAPH GRAMMARS: An Algebraic Approach, Proc. IEEE Conf. on Automata and Switching Theory, Iowa City 1973, 167–180Google Scholar
  5. /ER 76a/.
    Ehrig, H., Rosen, B.K.: Commutativity of Independent Transformations on Complex Objects, IBM Research Report, RC 6251, Oct 1976Google Scholar
  6. /ER 76b/.
    Ehrig, H., Rosen, B.K.: The Mathematics of Record Handling (in preparation)Google Scholar
  7. /FKZ 76/.
    Farrow, R., Kennedy, K., Zucconi, L.: Graph Grammars and Global Program Data Flow Analysis, Proc. 17th Ann. IEEE Symp. on Foundations of Comp. Sci., Houston, 1976Google Scholar
  8. /Fr 75/.
    Franck, R.: PLAN2D — Syntaxanalyse von Präzedenz-Graph-Grammatiken, Dissertation, Technische Universität Berlin, FB 20, 1975Google Scholar
  9. /Gr 68/.
    Griffiths, T.V.: Some Remarks on Derivations in General Rewriting Systems, Information and Control 12, 1968, 27–54Google Scholar
  10. /Kr 76/.
    Kreowski, H.-J.: Kanonische Ableitungssequenzen für Graph-Grammatiken, Research Report, FB 20, Techn. Univ. Berlin, 76-26Google Scholar
  11. /Ro 73/.
    Rosen, B.K.: Tree-Manipulating System and Church-Rosser Theorems, Journ. ACM 20, 1, 1973, 160–187Google Scholar
  12. /Ro 74/.
    —: Correctness of Parallel Programs: The Church-Rosser Approach, Theoretical Comp. Sci. 2, 1976, 183–207Google Scholar
  13. /Ro 75a/.
    — A Church-Rosser Theorem for Graph-Grammars (announcement), STGACT News 7, 3, 1975, 26–31Google Scholar
  14. /Ro 75b/.
    —: Deriving Graphs from Graphs by Applying a Production, Acta Informatica 4, 1975, 337–357Google Scholar
  15. /Sch 76/.
    Schneider, H.J.: Conceptual Data Base Description Using Graph Grammars, to appear in: Proc. Workshop "Graphentheoretische Konzepte in der Informatik", Göttingen, 1976Google Scholar
  16. /Se 74/.
    Sethi, R.: Testing for the Church-Rosser Property, Journ. ACM 21, 4, 1974, 671–679Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Hans-Jörg Kreowski
    • 1
  1. 1.Fachbereich Informatik (20)Technische Universität BerlinBerlin 10Germany

Personalised recommendations