Abstract
Let B-edNCE and C-edNCE denote the families of graph languages generated by boundary and by confluent edNCE graph grammars, respectively. Boundary means that two nonterminals are never adjacent, and confluent means that rewriting steps are order independent. By definition, boundary graph grammars are confluent, so that B-edNCE \(\subseteq\) C-edNCE. Engelfriet et. al. [8] have shown that this inclusion is proper, in general, using certain graph languages of unbounded degree as a witness. We prove that equality holds on graph languages of bounded degree, i.e., B-edNCEdeg=C-edNCEdeg, where the subscript “deg” refers to graph languages of bounded degree. Thus, for bounded degree, boundary graph grammars are the operator normal form of confluent graph grammars and e.g., the characterization results obtained independently for B-edNCE and C-edNCE can be merged. Our result confirms boundary and confluent graph grammars as notions for context-free graph grammars.
This research was supported in part by the Deutsche Forschungsgemeinschaft under Br 835/1.
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References
F.J. Brandenburg, “On partially ordered graph grammars”, Lecture Notes in Computer Science 291 (1987), 99–111.
F.J. Brandenburg, “On polynomial time graph grammars” Lecture Notes in Computer Science 294 (1988), 227–236
B. Courcelle, “An axiomatic definition of context-free rewriting and its applications” Theoret. Comput. Sci. 55 (1987), 141–181.
B. Courcelle, J. Engelfriet and G. Rozenberg, “Handle-rewriting hypergraph grammars”, Techn. Report, University of Leiden and University of Bordeaux (1990)
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)
J. Engelfriet, “Context-free NCE graph grammars” Proc. FCT 1989, Lecture Notes in Computer Science 380 (1989), 148–161
J. Engelfriet and G. Leih, “Complexity of boundary graph grammars” RAIRO Theoret. Inform. Appl.24, (1990), 267–274
J. Engelfriet, G. Leih, and E. Welzl, “Boundary graph grammars with dynamic edge relabeling”, Techn. Report, University of Leiden (1988), J. Comput. System Sci. to appear.
J. Engelfriet and G. Rozenberg, “A comparison of boundary graph grammars and context-free hypergraph grammars, Inform. Comput. 84 (1990), 163–206.
M. Harrison, “Introduction to Formal Language Theory”, Addison Wesley, 1978
D. Janssens, G. Rozenberg and E. Welzl, “The bounded degree problem for NLC grammars is decidable”, J. Comput. System Sci. 33 (1986), 415–422.
G. Rozenberg and E. Welzl, “Boundary NLC graph grammars-basic definitions, normal forms and complexity”, Inform. Control 69 (1986), 131–167.
G. Rozenberg and E. Welzl, “Combinatorial properties of boundary NLC graph languages”, Discrete Appl. Math. 16 (1987), 58–73
R. Schuster, “Graphgrammatiken und Grapheinbettungen: Algorithmen und Komplexität” Ph.D. Thesis and MIP-8711 Report, Universität Passau (1987).
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© 1991 Springer-Verlag Berlin Heidelberg
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Brandenburg, F.J. (1991). The equivalence of boundary and confluent graph grammars on graph languages of bounded degree. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_106
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DOI: https://doi.org/10.1007/3-540-53904-2_106
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