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.
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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).
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.
H. Ehrig, H.-J. Kreowski and G. Rozenberg (Eds.), Graph-Grammars and Their Application to Computer Science, Lecture Notes in Computer Science 153(1982).
H. Ehrig, H.-J. Kreowski and G. Rozenberg (Eds.), Graph-Grammars and Their Application to Computer Science, Lecture Notes in Computer Science 532(1991).
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).
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.
Y. Kawahara, Pushout-complements and basic concepts of grammars in toposes, Theoret. Comput. Sci. 77(1990), 267–289.
Y. Kawahara and Y. Mizoguchi, Categorical assertion semantics in topoi, Advances in Software Science and Technology, 4(1992), 137–150.
R. Kennaway, Graph rewriting in some categories of partial morphisms, Lecture Notes in Computer Science 532(1991), 490–504.
M. Löwe and H. Ehrig, Algebraic approach to graph transformation based on single pushout derivations, Lecture Notes in Computer Science 484(1991), 338–353.
S. Mac Lane, Categories for the Working Mathematician, (Springer-Verlag, 1972).
Y. Mizoguchi, A graph structure over the category of sets and partial functions, to appear in Cahiers de topologie et géométorie différentielle catégoriques.
Y. Mizoguchi and Y. Kawahara, Relational graph rewritings, to appear in TCS.
J. C. Raoult, On graph rewritings, Theoret. Comput. Sci. 32(1984), 1–24.
E. Robinson and G. Rosolini, Categories of partial maps, Inf. Comp. 79(1988), 95–130.
P.M. van den Broek, Algebraic graph rewtiting using a single pushouts, Lecture Notes in Computer Science 493(1991), 90–102.
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© 1994 Springer-Verlag Berlin Heidelberg
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Kawahara, Y., Mizoguchi, Y. (1994). Relational structures and their partial morphisms in view of single pushout rewriting. In: Schneider, H.J., Ehrig, H. (eds) Graph Transformations in Computer Science. Lecture Notes in Computer Science, vol 776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57787-4_14
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DOI: https://doi.org/10.1007/3-540-57787-4_14
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