Abstract
Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. Towards a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot define all regular tree languages, or equivalently, all of monadic second-order logic. We prove this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot define all regular languages. We then extend this result to a class of TWAs that can simulate first-order logic (FO) and is capable of expressing properties not definable in FO extended with regular path expressions; the latter logic being a valid abstraction of current query languages for XML and semi-structured data.
Research Assistant of the Fund for Scientific Research, Flanders.
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References
S. Abiteboul, P. Buneman, and D. Suciu. Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann, 1999.
A. V. Aho and J. D. Ullman. Translations on a context-free grammar. Inform, and Control, 19:439–475, 1971.
Y. Bargury and J. A. Makowsky. The expressive power of transitive closure logic and 2-way multi-head automata. In E. Borger, G. Jäger, H. K. Buning, and M. M. Richter editors. Computer Science Logic, volume 626 of Lecture Notes in Computer Science, pages 1–14. Springer-Verlag, 1991.
G. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Submitted.
R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. To appear in the Journal of Computer and System Sciences.
A. Brüggeman-Klein, S. Hermann, and D. Wood. Context, caterpillars, tree automata, and tree pattern matching. In Proceedings of the 4th International Conference on Developments in Language Theory, 1999.
J. Clark. XSL Transformations version 1.0. http://www.w3.org/TR/xslt.
J. Engelfriet and H. J. Hoogeboom. Tree-walking pebble automata. In J. Karhumäki, H. Maurer, G. Paun, and G. Rozenberg, editors, Jewels are forever, contributions to Theoretical Computer Science in honor of Arto Salomaa, pages 72–83. Springer-Verlag, 1999.
J. Engelfriet and H. J. Hoogeboom. Private communication.
J. Engelfriet, H.J. Hoogeboom, and J.-P. van Best. Trips on trees. Acta Cybernetica, 14:51–64, 1999.
Z. Fülöp and S. Maneth. Domains of partial attributed tree transducers. Information Processing Letters, 175–180, 2000.
H. Gaifman. On local and nonlocal properties. In J. Stern, editor, Logic Colloquium’ 81, pages 105–135. North Holland, 1982.
F. Gécseg and M. Steinby. Tree languages. In A. Salomaa, editors. Handbook of Formal Languages. Springer, 1997 [19], chapter 1.
T. Kamimura and G. Slutzki. Parallel and two-way automata on directed ordered acyclic graphs. Information and Control, 49(1): 10–51, April 1981.
T. Milo, D. Suciu, and V. Vianu. Type checking for XML transformers. Proceedings of the 19th ACM Symposium on Principles of Database Systems, 2000.
F. Neven. Design and Analysis of Query Languages for Structured Documents — A Formal and Logical Approach. Doctor’s thesis, Limburgs Universitair Centrum, 1999.
F. Neven and T. Schwentick. Expressive and efficient pattern languages for tree-structured data. Proceedings of the 19th ACM Symposium on Principles of Database Systems, 2000.
A. Potthoff. Logische Klassifizierung regulärer Baumsprachen. Doctor’s thesis, Institut für Informatik u. Prakt. Math., Universität Kiel, 1994.
G. Rozenberg and A. Salomaa, editors. Handbook of Formal Languages. Springer, 1997.
W. Thomas. Languages, automata, and logic. In A. Salomaa, editors. Handbook of Formal Languages. Springer, 1997 [19], chapter 7.
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Neven, F., Schwentick, T. (2000). On the Power of Tree-Walking Automata. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_46
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DOI: https://doi.org/10.1007/3-540-45022-X_46
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