Transition Graphs of Rewriting Systems over Unranked Trees

  • Christof Löding
  • Alex Spelten
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


We investigate algorithmic properties of infinite transition graphs that are generated by rewriting systems over unranked trees. Two kinds of such rewriting systems are studied. For the first, we construct a reduction to ranked trees via an encoding and to standard ground tree rewriting, thus showing that the generated classes of transition graphs coincide. In the second rewriting formalism, we use subtree rewriting combined with a new operation called flat prefix rewriting and show that strictly more transition graphs are obtained while the first-order theory with reachability relation remains decidable.


Infinite graphs reachability rewriting unranked trees 


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  1. 1.
    Blumensath, A.: Automatic Structures. Diploma thesis, RWTH Aachen, Germany (1999),
  2. 2.
    Brainerd, W.: Tree generating regular systems. Inf. and Contr. 14(2), 217–231 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and regular hedge languages over unranked alphabets. Unfinished technical report, Hongkong University (April 2001),
  4. 4.
    Carme, J., Nieren, J., Tommasi, M.: Querying unranked trees with stepwise tree automata. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 105–118. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Caucal, D.: On the regular structure of prefix rewriting. TCS 106(1), 61–86 (1992)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Caucal, D.: On infinite terms having a decidable theory. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 165–176. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (Unpublished electronic book, 1997),
  8. 8.
    Coquidé, J.-L., Dauchet, M., Gilleron, R., Vágvölgyi, S.: Bottom-up tree pushdown automata: classification and connection with rewrite systems. TCS 127(1), 69–98 (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    Courcelle, B.: A representation of trees by languages. TCS 7, 25–55 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dauchet, M., Tison, S.: The theory of ground rewrite systems is decidable. In: Proc. LICS 1990, pp. 242–248. IEEE CSP, Los Alamitos (1990)Google Scholar
  11. 11.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of TCS, pp. 995–1072. Elsevier, Amsterdam (1990)Google Scholar
  12. 12.
    Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley, Boston (2001)zbMATHGoogle Scholar
  13. 13.
    Löding, C.: Ground tree rewriting graphs of bounded tree width. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 559–570. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Löding, C.: Model-checking infinite systems generated by ground tree rewriting. In: Nielsen, M., Engberg, U. (eds.) ETAPS 2002 and FOSSACS 2002. LNCS, vol. 2303, pp. 280–294. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Löding, C.: Infinite Graphs Generated by Tree Rewriting. PhD thesis, RWTH Aachen, Germany (2003)Google Scholar
  16. 16.
    Seese, D.: Entscheidbarkeits- und Definierbarkeitsfragen der Theorie, netzartiger Graphen-I. Wiss. Zeitschrift HU Berlin, XXI(5), 513–517 (1972)Google Scholar
  17. 17.
    Spelten, A.: Rewriting Systems over Unranked Trees. Diploma thesis, RWTH Aachen, Germany (2006),
  18. 18.
    Takahashi, M.: Generalizations of regular sets and their application to a study of context-free languages. Inf. and Contr. 27(1), 1–36 (1975)zbMATHCrossRefGoogle Scholar
  19. 19.
    Thomas, W.: A short introduction to infinite automata. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol. 2295, pp. 130–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Christof Löding
    • 1
  • Alex Spelten
    • 1
  1. 1.RWTH AachenGermany

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