Abstract
A necessary and sufficient condition for termination of graph rewriting systems is established. Termination is equivalent to the finiteness of all forward closures, being certain minimal derivations in which each step depends on previous steps. This characterization differs from corresponding results for term rewriting in that the latter hold only for subclasses of term rewriting systems. When applied to term graph rewriting, the result characterizes termination of arbitrary term rewriting systems under graph rewriting. In particular, it captures non-terminating term rewriting systems that are terminating under graph rewriting.
Research partially supported by ESPRIT Basic Research Working Group 6112, COMPASS
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Hendrik Barendregt, Marko van Eekelen, John Glauert, Richard Kennaway, Rinus Plasmeijer, and Ronan Sleep. Term graph rewriting. In Proc. Parallel Architectures and Languages Europe, pages 141–158. Springer Lecture Notes in Computer Science 259, 1987.
Andrea Corradini and Francesca Rossi. Hyperedge replacement jungle rewriting for term rewriting systems and logic programming. Theoretical Computer Science, 109:7–48, 1993.
Nachum Dershowitz. Termination of linear rewriting systems (preliminary version). In Proc. Automata, Languages, and Programming, pages 448–458. Springer Lecture Notes in Computer Science 115, 1981.
Nachum Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69–116, 1987.
Hartmut Ehrig. Introduction to the algebraic theory of graph grammars. In Proc. Graph-Grammars and Their Application to Computer Science and Biology, pages 1–69. Springer Lecture Notes in Computer Science 73, 1979.
Hartmut Ehrig and Hans-Jörg Kreowski. Parallelism of manipulations in multidimensional information structures. In Proc. Mathematical Foundations of Computer Science, pages 284–293. Springer Lecture Notes in Computer Science 45, 1976.
Oliver Geupel. Overlap closures and termination of term rewriting systems. Report MIP-8922, FakultÄt für Mathematik und Informatik, UniversitÄt Passau, Passau, Germany, 1989.
Annegret Habel. Hypergraph grammars: Transformational and algorithmic aspects. Journal of Information Processing and Cybernetics, 5:241–277, 1992.
Berthold Hoffmann and Detlef Plump. Implementing term rewriting by jungle evaluation. RAIRO Theoretical Informatics and Applications, 25(5):445–472, 1991.
Hans-Jörg Kreowski. Manipulationen von Graphmanipulationen. Dissertation, Technische UniversitÄt Berlin, 1977.
Detlef Plump. Evaluation of functional expressions by hypergraph rewriting. Dissertation, UniversitÄt Bremen, Fachbereich Mathematik und Informatik, 1993.
Neil Robertson and P.D. Seymour. Graph minors — a survey. In Ian Anderson, editor, Surveys in Combinatorics 1985, pages 153–171. London Mathematical Society, 1985.
Ronan Sleep, Rinus Plasmeijer, and Marko van Eekelen, editors. Term Graph Rewriting: Theory and Practice. John Wiley, 1993.
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© 1995 Springer-Verlag Berlin Heidelberg
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Plump, D. (1995). On termination of graph rewriting. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1995. Lecture Notes in Computer Science, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60618-1_68
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DOI: https://doi.org/10.1007/3-540-60618-1_68
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