Bottom-Up Tree Automata with Term Constraints

  • Andreas Reuß
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


We introduce bottom-up tree automata with equality and disequality term constraints. These constraints are more expressive than the equality and disequality constraints between brothers introduced by Bogaert and Tison in 1992. Our new class of automata is still closed under Boolean operations. Moreover, we show that for tree automata with term constraints not only membership but also emptiness is decidable. This contrasts with the undecidability of emptiness for automata with arbitrary equality constraints between subterms identified by paths as shown in 1981 by Mongy.


Equality Constraint Horn Clause Disjunctive Normal Form Tree Automaton Tree Language 
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  1. 1.
    Barguño, L., Creus, C., Godoy, G., Jacquemard, F., Vacher, C.: The emptiness problem for tree automata with global constraints. In: Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science (LICS 2010), Edinburgh, Scotland, UK, July 2010. IEEE Computer Society Press, Los Alamitos (2010), (to appear)
  2. 2.
    Bogaert, B., Tison, S.: Equality and disequality constraints on direct subterms in tree automata. In: STACS 1992: Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science, London, UK, pp. 161–171. Springer, Heidelberg (1992) ISBN 3-540-55210-3Google Scholar
  3. 3.
    Caron, A.-C., Comon, H., Coquidé, J.-L., Dauchet, M., Jacquemard, F.: Pumping, cleaning and symbolic constraints solving. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 436–449. Springer, Heidelberg (1994), ISBN 3-540-58201-0 CrossRefGoogle Scholar
  4. 4.
    Caron, A.-C., Coquidé, J.-L., Dauchet, M.: Encompassment properties and automata with constraints. In: Kirchner, C. (ed.) RTA 1993. LNCS, vol. 690, pp. 328–342. Springer, Heidelberg (1993), ISBN 3-540-56868-9CrossRefGoogle Scholar
  5. 5.
    Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007), (release October 12, 2007)
  6. 6.
    Comon, H., Jacquemard, F.: Ground reducibility is exptime-complete. In: LICS 1997: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, Washington, DC, USA, p. 26. IEEE Computer Society, Los Alamitos (1997) ISBN 0-8186-7925-5Google Scholar
  7. 7.
    Comon, H., Jacquemard, F.: Ground reducibility and automata with disequality constraints. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 151–162. Springer, Heidelberg (1994), ISBN 3-540-57785-8CrossRefGoogle Scholar
  8. 8.
    Filiot, E., Talbot, J.-M., Tison, S.: Tree automata with global constraints. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 314–326. Springer, Heidelberg (2008), ISBN 978-3-540-85779-2, doi:
  9. 9.
    Frühwirth, T.W., Shapiro, E.Y., Vardi, M.Y., Yardeni, E.: Logic programs as types for logic programs. In: LICS, pp. 300–309 (1991)Google Scholar
  10. 10.
    Godoy, G., Giménez, O., Ramos, L., Àlvarez, C.: The hom problem is decidable. In: STOC, pp. 485–494 (2010)Google Scholar
  11. 11.
    Löding, C., Wong, K.: On nondeterministic unranked tree automata with sibling constraints. In: FSTTCS, pp. 311–322 (2009)Google Scholar
  12. 12.
    Mongy, J.: Transformation de noyaux reconnaissables d’arbres. PhD thesis, Laboratoire d’Informatique Fondamentale de Lille, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France (1981)Google Scholar
  13. 13.
    Tommasi, M.: Automates d’arbres avec tests d’égalité entre cousins germains. Mémoire de DEA, Univ. Lille I (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andreas Reuß
    • 1
  • Helmut Seidl
    • 1
  1. 1.Institut für Informatik I2Technische Universität MünchenGarching

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