Advertisement

Relational structures and their partial morphisms in view of single pushout rewriting

  • Yasuo Kawahara
  • Yoshihiro Mizoguchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 776)

Abstract

In this paper we present a basic notion of relational structures which includes simple graphs, labelled graphs and hypergraphs, and introduce a notion of partial morphisms between them. An existence theorem of pushouts in the category of relational structures and their partial morphisms is proved under a certian functorial condition, and it enables us to discuss single pushout rewritings of relational structures.

Keywords

Relational Structure Production Rule Natural Transformation Partial Function Simple Graph 
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. 1.
    V. Claus, H. Ehrig and G. Rozenberg (Eds.), Graph-Grammars and Their Application to Computer Science and Biology, Lecture Notes in Computer Science 73(1979).Google Scholar
  2. 2.
    H. Ehrig, H.-J. Kreowski, A. Maggiolo-Schettini, B. K. Rosen and J. Winkowski, Transformations of structures: an algebraic approach, Math. Systems Theory 14(1981), 305–334.CrossRefGoogle Scholar
  3. 3.
    H. Ehrig, H.-J. Kreowski and G. Rozenberg (Eds.), Graph-Grammars and Their Application to Computer Science, Lecture Notes in Computer Science 153(1982).Google Scholar
  4. 4.
    H. Ehrig, H.-J. Kreowski and G. Rozenberg (Eds.), Graph-Grammars and Their Application to Computer Science, Lecture Notes in Computer Science 532(1991).Google Scholar
  5. 5.
    H. Ehrig, M. Nagl, G. Rozenberg and A. Rosenfeld (Eds.), Graph-Grammars and Their Application to Computer Science, Lecture Notes in Computer Science 291(1987).Google Scholar
  6. 6.
    H. Ehrig, H. Pfender and H.J. Schneider, Graph grammars: an algebraic approach, Proc. 14th Ann. Conf. on Switching and Automata Theory (1973), 167–180.Google Scholar
  7. 7.
    Y. Kawahara, Pushout-complements and basic concepts of grammars in toposes, Theoret. Comput. Sci. 77(1990), 267–289.Google Scholar
  8. 8.
    Y. Kawahara and Y. Mizoguchi, Categorical assertion semantics in topoi, Advances in Software Science and Technology, 4(1992), 137–150.Google Scholar
  9. 9.
    R. Kennaway, Graph rewriting in some categories of partial morphisms, Lecture Notes in Computer Science 532(1991), 490–504.Google Scholar
  10. 10.
    M. Löwe and H. Ehrig, Algebraic approach to graph transformation based on single pushout derivations, Lecture Notes in Computer Science 484(1991), 338–353.Google Scholar
  11. 11.
    S. Mac Lane, Categories for the Working Mathematician, (Springer-Verlag, 1972).Google Scholar
  12. 12.
    Y. Mizoguchi, A graph structure over the category of sets and partial functions, to appear in Cahiers de topologie et géométorie différentielle catégoriques.Google Scholar
  13. 13.
    Y. Mizoguchi and Y. Kawahara, Relational graph rewritings, to appear in TCS.Google Scholar
  14. 14.
    J. C. Raoult, On graph rewritings, Theoret. Comput. Sci. 32(1984), 1–24.Google Scholar
  15. 15.
    E. Robinson and G. Rosolini, Categories of partial maps, Inf. Comp. 79(1988), 95–130.Google Scholar
  16. 16.
    P.M. van den Broek, Algebraic graph rewtiting using a single pushouts, Lecture Notes in Computer Science 493(1991), 90–102.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yasuo Kawahara
    • 1
  • Yoshihiro Mizoguchi
    • 2
  1. 1.Research Institute of Fundamental Information ScienceKyushu University 33FukuokaJapan
  2. 2.Deptartment of Control Engineering and ScienceKyushu Institute of TechnologyIizukaJapan

Personalised recommendations