Abstract
We investigate bottom-up and top-down deterministic automata on unranked trees. We show that for an appropriate definition of bottom-up deterministic automata it is possible to minimize the number of states efficiently and to obtain a unique canonical representative of the accepted tree language. For top-down deterministic automata it is well known that they are less expressive than the non-deterministic ones. By generalizing a corresponding proof from the theory of ranked tree automata we show that it is decidable whether a given regular language of unranked trees can be recognized by a top-down deterministic automaton. The standard deterministic top-down model is slightly weaker than the model we use, where at each node the automaton can scan the sequence of the labels of its successors before deciding its next move.
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References
Berstel, J., Boasson, L.: Formal properties of XML grammars and languages. Acta Informatica 38, 649–671 (2002)
Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)
Brüggemann-Klein, A., Wood, D., Murata, M.: Regular tree and regular hedge languages over unranked alphabets: Version 1. unfinished technical report (April 2001), http://citeseer.ist.psu.edu/451005.html
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications. Unpublished electronic book (1997), http://www.grappa.univ-lille3.fr/tata
Eilenberg, S.: Automata, languages, and machines, vol. A. Academic Press, London (1974)
Gécseg, F., Steinby, M.: Tree automata. Akadémiai Kiadò, Budapest (1984)
Hopcroft, J.E.: An nlogn algorithm for minimizing states in a finite automaton. Theory of Machines and Computations, pp. 189–196 (1971)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Reading (1979)
Martens, W., Neven, F., Schwentick, T.: Which XML schemas admit 1-pass preorder typing? In: Eiter, T., Libkin, L. (eds.) ICDT 2005. LNCS, vol. 3363, pp. 68–82. Springer, Heidelberg (2004)
Milo, T., Suciu, D., Vianu, V.: Typechecking for XML transformers. Journal of Computer and System Sciences 66(1), 66–97 (2003)
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)
Neven, F., Schwentick, T.: Query automata on finite trees. Theoretical Computer Science 275, 633–674 (2002)
Suciu, D.: Typechecking for semistructured data. In: Ghelli, G., Grahne, G. (eds.) DBPL 2001. LNCS, vol. 2397, pp. 1–20. Springer, Heidelberg (2002)
Virágh, J.: Deterministic ascending tree automata I. Acta Cybernet 5, 33–42 (1980)
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Cristau, J., Löding, C., Thomas, W. (2005). Deterministic Automata on Unranked Trees. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_7
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DOI: https://doi.org/10.1007/11537311_7
Publisher Name: Springer, Berlin, Heidelberg
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