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Graph grammars and tree transducers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 787))

Abstract

Regular tree grammars can be used to generate graphs, by generating expressions that denote graphs. Top-down and bottom-up tree transducers are a tool for proving properties of such graph generating tree grammars.

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References

  1. M.Bauderon, B.Courcelle; Graph expressions and graph rewritings, Math. Syst. Theory 20 (1987), 83–127

    Article  Google Scholar 

  2. F.J.Brandenburg; On polynomial time graph grammars, Proc. STACS 88, Lecture Notes in Computer Science 294, Springer-Verlag, Berlin, pp.227–236

    Google Scholar 

  3. F.J.Brandenburg; The equivalence of boundary and confluent graph grammars on graph languages of bounded degree, in Rewriting Techniques and Applications (R.V.Book, ed.), Lecture Notes in Computer Science 488, Springer-Verlag, Berlin, 1991, pp.312–322

    Google Scholar 

  4. D.G.Corneil, H.Lerchs, L.Stewart Burlingham; Complement reducible graphs, Discr. Appl. Math. 3 (1981), 163–174

    Article  Google Scholar 

  5. B.Courcelle; An axiomatic definition of context-free rewriting and its application to NLC graph grammars, Theor. Comput. Sci. 55 (1987), 141–181

    Article  Google Scholar 

  6. B.Courcelle; The monadic second-order logic of graphs I: Recognizable sets of finite graphs, Inform. and Comput. 85 (1990), 12–75

    Article  Google Scholar 

  7. B.Courcelle; Graph rewriting: an algebraic and logic approach, in Formal Models and Semantics, Handbook of Theoretical Computer Science Volume B (J.vanLeeuwen, ed.), Elsevier, Amsterdam, 1990, pp.193–242

    Google Scholar 

  8. B.Courcelle; On the structure of context-free sets of graphs generated by vertex replacement, Report 91-44, Bordeaux-1 University (A short version is Contextfree graph grammars: separating vertex replacement from hyperedge replacement, Proc. FCT'93 (Z.Ésik, ed.), Lecture Notes in Computer Science 710, Springer-Verlag, Berlin, pp.181–193)

    Google Scholar 

  9. B.Courcelle; Graph grammars, monadic second-order logic and the theory of graph minors, in Proc. of the A.M.S. Conference on Graph Minors, Seattle, 1993 (preliminary version in Bulletin of the EATCS 46 (1992), 193–226)

    Google Scholar 

  10. B.Courcelle; The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Theor. Comput. Sci. 80 (1991), 153–202

    Article  Google Scholar 

  11. B.Courcelle; Monadic second-order definable graph transductions, invited lecture, Proc.CAAP '92 (J.-C.Raoult, ed.), Lecture Notes in Computer Science 581, Springer-Verlag, Berlin, 1992

    Google Scholar 

  12. B.Courcelle; The monadic second-order logic of graphs VII: Graphs as relational structures, Theor. Comput. Sci. 101 (1992), 3–33

    Article  Google Scholar 

  13. B.Courcelle; Recognizable sets of graphs: equivalent definitions and closure properties, Research Report 92-06, Bordeaux-1 University

    Google Scholar 

  14. B.Courcelle, J.Engelfriet; A logical characterization of the sets of hypergraphs generated by hyperedge replacement grammars, Research Report 91-41, Bordeaux-1 University, to appear in Math. Syst. Theory.

    Google Scholar 

  15. B.Courcelle, J.Engelfriet, G.Rozenberg; Handle-rewriting hypergraph grammars, J. Comp. Syst. Sci. 46 (1993), 218–270

    Article  Google Scholar 

  16. B.Courcelle, M.Mosbah; Monadic second-order evaluations on tree-decomposable graphs, Theor. Comput. Sci. 109 (1993), 49–82

    Article  Google Scholar 

  17. F.Drewes; Transducibility — symbolic computation by tree-transductions, Universität Bremen, Bericht Nr: 2/93, 1993

    Google Scholar 

  18. F.Drewes, H.-J.Kreowski; A note on hyperedge replacement, in [19], pp. 1–11

    Google Scholar 

  19. H.Ehrig, H.-J.Kreowski, G.Rozenberg (eds.); Graph-Grammars and their Application to Computer Science, Lecture Notes in Computer Science 532, Springer-Verlag, Berllin, 1991

    Google Scholar 

  20. H.Ehrig, M.Nagl, G.Rozenberg, A.Rosenfeld (eds.); Graph-Grammars and their Application to Computer Science, Lecture Notes in Computer Science 291, Springer-Verlag, Berlin, 1987

    Google Scholar 

  21. J.Engelfriet; Tree automata and tree grammars, Lecture Notes, DAIMI FN-10, Aarhus, 1975

    Google Scholar 

  22. J.Engelfriet; Top-down tree transducers with regular look-ahead, Math. Syst. Theory 10 (1977), 289–303

    Article  Google Scholar 

  23. J.Engelfriet; Some open questions and recent results on tree transducers and tree languages, in Formal language theory; perspectives and open problems (R.V.Book, ed.), Academic Press, New York, 1980

    Google Scholar 

  24. J.Engelfriet; Context-free NCE graph grammars, Proc. FCT '89, Lecture Notes in Computer Science 380, Springer-Verlag, Berlin, pp.148–161

    Google Scholar 

  25. J.Engelfriet; A characterization of context-free NCE graph languages by monadic second-order logic on trees, in [19], pp.311–327

    Google Scholar 

  26. J.Engelfriet; A Greibach normal form for context-free graph grammars, Proc. ICALP '92 (W.Kuich, ed.), Lecture Notes in Computer Science 623, Springer-Verlag, Berlin, pp.138–149

    Google Scholar 

  27. J.Engelfriet, L.M.Heyker; Hypergraph languages of bounded degree, Report 91-01, Leiden University, to appear in J. Comp. Syst. Sci.

    Google Scholar 

  28. J.Engelfriet, L.M.Heyker, G.Leih; Context-free graph languages of bounded degree are generated by apex graph grammars, Report 91-16, Leiden University, to appear in Acta Informatica

    Google Scholar 

  29. J.Engelfriet, G.Leih, G.Rozenberg; Nonterminal separation in graph grammars, Theor. Comput: Sci. 82 (1991), 95–111

    Article  Google Scholar 

  30. J.Engelfriet, G.Rozenberg; A comparison of boundary graph grammars and context-free hypergraph grammars, Inform. and Comput. 84 (1990), 163–206

    Article  Google Scholar 

  31. F.Gécseg, M.Steinby; Tree automata, Akadémiai Kiadó, Budapest, 1984

    Google Scholar 

  32. A.Habel; Hyperedge replacement: grammars and languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992

    Google Scholar 

  33. A.Habel, H.-J.Kreowski; May we introduce to you: hyperedge replacement, in [20], pp. 15–26

    Google Scholar 

  34. A.Habel, H.-J.Kreowski, C.Lautemann; A comparison of compatible, finite, and inductive graph properties, Theor. Comput. Sci. 110 (1993), 145–168

    Article  Google Scholar 

  35. A.Habel, H.-J.Kreowski, W.Vogler; Metatheorems for decision problems on hyperedge replacement graph languages, Acta Informatica 26 (1989), 657–677

    Article  Google Scholar 

  36. A.Habel, H.-J.Kreowski, W.Vogler; Decidable boundedness problems for sets of graphs generated by hyperedge-replacement, Theor. Comput. Sci. 89 (1991), 33–62

    Article  Google Scholar 

  37. M.Kaul; Syntaxanalyse von Graphen bei Präzedenz-Graph-Grammatiken, Ph. D. Thesis, Osnabrück, 1985

    Google Scholar 

  38. S.Kuske; A maximum path length pumping lemma for edge-replacement languages, Proc. FCT'93 (Z.Ésik, ed.), Lecture Notes in Computer Science 710, Springer-Verlag, Berlin, pp.342–351

    Google Scholar 

  39. T.Lengauer, E.Wanke; Efficient decision procedures for graph properties on context-free graph languages, J. of the ACM 40 (1993), 368–393

    Article  Google Scholar 

  40. J.Mezei, J.B.Wright; Algebraic automata and context-free sets, Inform. and Control 11 (1967), 3–29

    Article  Google Scholar 

  41. M.Nagl; Graph-Grammatiken, Vieweg, Braunschweig, 1979

    Google Scholar 

  42. M.Nivat, A.Podelski (eds.); Tree automata and languages, North-Holland, Amsterdam, 1992

    Google Scholar 

  43. W.C.Rounds; Mappings and grammars on trees, Math. Syst. Theory 4 (1970), 257–287

    Article  Google Scholar 

  44. R.Schuster; Graphgrammatiken und Grapheinbettungen: Algorithmen und Komplexität, Ph.D.Thesis, Report MIP-8711, Passau, 1987

    Google Scholar 

  45. H.Seidl; Finite tree automata with cost functions, Proc. CAAP'92 (J.-C.Raoult, ed.), Lecture Notes in Computer Science 581, Springer-Verlag, Berlin, pp.279–299

    Google Scholar 

  46. W.Vogler; On hyperedge replacement and BNLC graph grammars, Discr. Appl. Math. 46 (1993), 253–273

    Article  Google Scholar 

  47. E.Wanke; On the decidability of integer subgraph problems on context-free graph languages, Proc. FCT '91 (L.Budach, ed.), Lecture Notes in Computer Science 529, Springer-Verlag, Berlin, pp.415–426

    Google Scholar 

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Sophie Tison

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© 1994 Springer-Verlag Berlin Heidelberg

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Engelfriet, J. (1994). Graph grammars and tree transducers. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017471

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  • DOI: https://doi.org/10.1007/BFb0017471

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57879-6

  • Online ISBN: 978-3-540-48373-1

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