Abstract
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.
The authors were supported by an FPU grant (first author) and the FORMALISM project (TIN2007-66523) from the Spanish Ministry of Education and Science.
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References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, New York (1998)
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)
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)
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)
Comon, H., Jacquemard, F.: Ground reducibility is EXPTIME-complete. Information and Computation 187(1), 123–153 (2003)
Comon, H., Cortier, V.: Tree automata with one memory, set constraints and cryptographic protocols. Theoretical Computer Science 331(1), 143–214 (2005)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Löding, C., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (2007), http://tata.gforge.inria.fr
Comon-Lundh, H., Jacquemard, F., Perrin, N.: Visibly tree automata with memory and constraints. Logical Methods in Computer Science 4(2:8) (2008)
Creus, C., Gascón, A., Godoy, G., Ramos, L.: The HOM problem is EXPTIME-complete. In: Logic in Computer Science (LICS), pp. 255–264 (2012)
Dauchet, M., Caron, A.C., Coquidé, J.L.: Automata for reduction properties solving. Journal of Symbolic Computation 20(2), 215–233 (1995)
Doner, J.: Tree acceptors and some of their applications. Journal of Computer System Sciences 4, 406–451 (1970)
Filiot, E., Talbot, J., Tison, S.: Tree automata with global constraints. International Journal of Foundations of Computer Science 21(4), 571–596 (2010)
Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó (1984)
Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 1–68. Springer (1997)
Godoy, G., Giménez, O.: The HOM problem is decidable. Journal of the ACM 60(4), 23 (2013)
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)
Mezei, J., Wright, J.B.: Algebraic automata and context-free sets. Information and Control 11, 3–29 (1967)
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)
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)
Treinen, R.: Predicate logic and tree automata with tests. In: Tiuryn, J. (ed.) FOSSACS 2000. LNCS, vol. 1784, pp. 329–343. Springer, Heidelberg (2000)
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Creus, C., Godoy, G. (2014). Tree Automata with Height Constraints between Brothers. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_11
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DOI: https://doi.org/10.1007/978-3-319-08918-8_11
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