We define the tree automata with height constraints between brothers (TACBB H ). Constraints of equalities and inequalities between heights of siblings that restrict the applicability of the rules are allowed in TACBB H . These constraints allow to express natural tree languages like complete or balanced (like AVL) trees. We prove decidability of emptiness and finiteness for TACBB H , and also for a more general class that additionally allows to combine equality and disequality constraints between brothers.


Tree-Automata Constraints Emptiness Finiteness 


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  1. 1.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, New York (1998)Google Scholar
  2. 2.
    Barguñó, L., Creus, C., Godoy, G., Jacquemard, F., Vacher, C.: Decidable classes of tree automata mixing local and global constraints modulo flat theories. Logical Methods in Computer Science 9(2) (2013)Google Scholar
  3. 3.
    Bogaert, B., Tison, S.: Equality and Disequality Constraints on Direct Subterms in Tree Automata. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 161–171. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  4. 4.
    Caron, A.-C., Seynhaeve, F., Tison, S., Tommasi, M.: Deciding the satisfiability of quantifier free formulae on one-step rewriting. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 103–117. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Comon, H., Jacquemard, F.: Ground reducibility is EXPTIME-complete. Information and Computation 187(1), 123–153 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Comon, H., Cortier, V.: Tree automata with one memory, set constraints and cryptographic protocols. Theoretical Computer Science 331(1), 143–214 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Löding, C., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (2007),
  8. 8.
    Comon-Lundh, H., Jacquemard, F., Perrin, N.: Visibly tree automata with memory and constraints. Logical Methods in Computer Science 4(2:8) (2008)Google Scholar
  9. 9.
    Creus, C., Gascón, A., Godoy, G., Ramos, L.: The HOM problem is EXPTIME-complete. In: Logic in Computer Science (LICS), pp. 255–264 (2012)Google Scholar
  10. 10.
    Dauchet, M., Caron, A.C., Coquidé, J.L.: Automata for reduction properties solving. Journal of Symbolic Computation 20(2), 215–233 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Doner, J.: Tree acceptors and some of their applications. Journal of Computer System Sciences 4, 406–451 (1970)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Filiot, E., Talbot, J., Tison, S.: Tree automata with global constraints. International Journal of Foundations of Computer Science 21(4), 571–596 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó (1984)Google Scholar
  14. 14.
    Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 1–68. Springer (1997)Google Scholar
  15. 15.
    Godoy, G., Giménez, O.: The HOM problem is decidable. Journal of the ACM 60(4), 23 (2013)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Jacquemard, F., Rusinowitch, M., Vigneron, L.: Tree automata with equality constraints modulo equational theories. Journal of Logic and Algebraic Programming 75(2), 182–208 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Mezei, J., Wright, J.B.: Algebraic automata and context-free sets. Information and Control 11, 3–29 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Mongy, J.: Transformation de noyaux reconnaissables d’arbres. Forêts RATEG. Ph.D. thesis, Laboratoire d’Informatique Fondamentale de Lille, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France (1981)Google Scholar
  19. 19.
    Murata, M., Lee, D., Mani, M., Kawaguchi, K.: Taxonomy of XML schema languages using formal language theory. ACM Transactions of Internet Technologies 5(4), 660–704 (2005)CrossRefGoogle Scholar
  20. 20.
    Treinen, R.: Predicate logic and tree automata with tests. In: Tiuryn, J. (ed.) FOSSACS 2000. LNCS, vol. 1784, pp. 329–343. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Carles Creus
    • 1
  • Guillem Godoy
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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