Abstract
We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSO-formulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deterministic automata, as in the ranked setting, is decidable. Furthermore, we show that the nondeterministic automata are more expressive than the deterministic ones.
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References
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)
Bojańczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. In: PODS 2006, pp. 10–19. ACM Press, New York (2006)
Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: LICS 2006, pp. 7–16. IEEE Computer Society Press, Los Alamitos (2006)
Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and regular hedge languages over unranked alphabets. Research Report HKUST-TCSC-2001-05, HKUST Theoretical Computer Science Center (2001), available on http://hdl.handle.net/1783.1/738
Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures. In: Handbook of Process Algebra, pp. 545–623. Elsevier, Amsterdam (2001)
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)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (1997) Current release: October 1st, 2002 Available on http://www.grappa.univ-lille3.fr/tata
Dal Zilio, S., Lugiez, D.: XML schema, tree logic and sheaves automata. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 246–263. Springer, Heidelberg (2003)
Dauchet, M., Caron, A.C., Coquidé, J.L.: Automata for reduction properties solving. Journal of Symbolic Computation 20, 215–233 (1995)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American Journal of Mathematics 35, 413–422 (1913)
Jacquemard, F., Rusinowitch, M., Vigneron, L.: Tree automata with equality constraints modulo equational theories. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 557–571. Springer, Heidelberg (2006)
Karianto, W., Löding, C.: Unranked tree automata with sibling equalities and disequalities. Technical Report AIB-2006-13, RWTH Aachen (2006)
Libkin, L.: Logics for unranked trees: An overview. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 35–50. Springer, Heidelberg (2005)
Lugiez, D.: Counting and equality constraints for multitree automata. In: Gordon, A.D. (ed.) ETAPS 2003 and FOSSACS 2003. LNCS, vol. 2620, pp. 328–342. Springer, Heidelberg (2003)
Mongy-Steen, J.: Transformation de noyaux reconnaissables d’arbres. Forêts RATEG. PhD thesis, Université de Lille I (1981)
Neven, F.: Automata, logic, and XML. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 2–26. Springer, Heidelberg (2002)
Seidl, H., Schwentick, T., Muscholl, A.: Numerical document queries. In: PODS 2003, pp. 155–166. ACM Press, New York (2003)
Seidl, H., Schwentick, T., Muscholl, A., Habermehl, P.: Counting in trees for free. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1136–1149. Springer, Heidelberg (2004)
Tommasi, M.: Automates d’arbres avec tests d’égalité entre cousins germains. Technical report, Mémoire de DEA, Université de Lille I (1992)
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Karianto, W., Löding, C. (2007). Unranked Tree Automata with Sibling Equalities and Disequalities. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_75
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DOI: https://doi.org/10.1007/978-3-540-73420-8_75
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