Abstract
In the algebraic theory of graph grammars, it is common practice to present some notions or results “up to isomorphism”. This allows one to reason about graphs and graph derivations without worrying about representation-dependent details.
Motivated by a research activity aimed at providing graph grammars with a truly-concurrent semantics, we front in this paper the problem of formalizing what does it mean precisely to reason about graph derivations “up to isomorphism”. This needs the definition of a suitable equivalence on derivations, which should be consistent with the relevant definitions and results, in the sense that they should extend to equivalence classes. After showing that a naive equivalence is not satisfactory, we propose two requirements for equivalences on derivations which allow the sequential composition of derivations and guarantee the uniqueness of canonical derivations, respectively. Three new equivalences are introduced, the third of which is shown to be satisfy both requirements. We also define a new category having the abstract derivations as arrows, which is, in our view, a fundamental step towards the definition of a truly-concurrent semantics for graph grammars.
Research partially supported by the COMPUGRAPH Basic Research Esprit Working Group n. 7183
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References
J. Adamek, H. Herrlich, G. Strecker, Abstract and Concrete Categories, Wiley Interscience, 1990.
A. Corradini, H. Ehrig, M. Lowe, U. Montanari, and F. Rossi, Note on Standard Representation of Graphs and Graph Derivations, in this volume. Also as Technical Report 92-25, Technische Universität Berlin, 1992.
H. Ehrig. Tutorial introduction to the algebraic approach of graph-grammars. In H. Ehrig, M. Nagl, G. Rozenberg, and A. Rosenfeld, editors, Proc. 3rd International Workshop on Graph Grammars and their Application to Computer Science, volume 291 of LNCS, pages 3–14. Springer-Verlag, 1987.
H. Ehrig, A. Habel, H.-J. Kreowski, F. Parisi-Presicce, Parallelism and Concurrency in High-Level Replacement Systems, in Mathematical Structures in Computer Science, 1, 1991, pp. 361–404.
H. Ehrig, M. Pfender, H.J. Schneider, Graph-grammars: an algebraic approach, Proc, IEEE Conf. on Automata and Switching Theory, 1973, pp. 167–180.
H.-J. Kreowski, Manipulation von Graph Transformationen, Ph.D. Thesis, Technische Universität Berlin, 1977.
M. Löwe, Extended algebraic graph transformation, Ph.D. Thesis, Technische Universität Berlin, 1990.
G. Winskel, An Introduction to Event Structures, in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of LNCS. Springer-Verlag, 1989. LNCS 354, 1989.
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© 1994 Springer-Verlag Berlin Heidelberg
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Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F. (1994). Abstract graph derivations in the double pushout approach. 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_6
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DOI: https://doi.org/10.1007/3-540-57787-4_6
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