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Ground Tree Rewriting Graphs of Bounded Tree Width

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We analyze structural properties of ground tree rewriting graphs, generated by rewriting systems that perform replacements at the front of finite, ranked trees. The main result is that the class of ground tree rewriting graphs of bounded tree width exactly corresponds to the class of pushdown graphs. Furthermore we show that ground tree rewriting graphs of bounded clique width also have bounded tree width.

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References

  1. Klaus Barthelmann. When can an equational simple graph be generated by hyperedge replacement? In Proceedings of MFCS’ 98, volume 1450 of LNCS, pages 543–552. Springer-Verlag, 1998.

    Google Scholar 

  2. Achim Blumensath and Erich Grädel. Automatic structures. In Proceedings of LICS’ 00, pages 51–62. IEEE Computer Society Press, 2000.

    Google Scholar 

  3. Achim Blumensath. Prefix-recognizable graphs and monadic second order logic. Technical Report AIB-2001-06, RWTH Aachen, May 2001.

    Google Scholar 

  4. Walter S. Brainerd. Tree generating regular systems. Information and Control, 14:217–231, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Caucal. On the regular structure of prefix rewriting. Theoretical Computer Science, 106(1):61–86, 1992.

    Article  MathSciNet  Google Scholar 

  6. Didier Caucal. On infinite transition graphs having a decidable monadic theory. In Proceedings of ICALP’ 96, volume 1099 of LNCS. Springer-Verlag, 1996.

    Google Scholar 

  7. J.L. Coquidé and R. Gilleron. Proofs and reachability problem for ground rewrite systems. In Aspects and Prospects of Theoretical Computer Science, volume 464 of LNCS, pages 120–129. Springer, 1990.

    Google Scholar 

  8. Bruno Courcelle and Stephan Olariu. Upper bounds to the clique width of graphs. Discrete Applied Mathematics, 101:77–114, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  9. Max Dauchet, Thierry Heuillard, Pierre Lescanne, and Sophie Tison. Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems. Information and Computation, 88(2):187–201, October 1990.

    Article  MATH  MathSciNet  Google Scholar 

  10. Reinhard Diestel. Graph Theory. Springer, second edition, 2000.

    Google Scholar 

  11. Max Dauchet and Sophie Tison. The theory of ground rewrite systems is decidable. In Proceedings of LICS’ 90, pages 242–248. IEEE Computer Society Press, 1990.

    Google Scholar 

  12. Frank Gurski and Egon Wanke. The tree-width of clique-width bounded graphs without Kn,n. In Proceedings of WG 2000, volume 1928 of LNCS, pages 196–205. Springer-Verlag, 2000.

    Google Scholar 

  13. Richard Mayr. Process rewrite systems. Information and Computation, 156(1–2):264–286, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  14. Christophe Morvan. On rational graphs. In Proceedings of FoSSaCS’ 99, volume 1784 of LNCS, pages 252–266. Springer, 1999.

    Google Scholar 

  15. David E. Muller and Paul E. Schupp. The theory of ends, pushdown automata, and second-order logic. Theoretical Computer Science, 37:51–75, 1985.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. RWTH Aachen, Aachen

    Christof Löding

Authors
  1. Christof Löding
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, TakustraĂźe 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Löding, C. (2002). Ground Tree Rewriting Graphs of Bounded Tree Width. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_46

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  • DOI: https://doi.org/10.1007/3-540-45841-7_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

  • eBook Packages: Springer Book Archive

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