In the XML standard, data are represented as unranked labeled ordered trees. Regular unranked tree automata provide a useful formalism for the validation of schemas enforcing regular structural constraints on XML documents. However some concrete application contexts need the expression of more general constraints than the regular ones. In this paper we propose a new framework in which context-free style structural constraints can be expressed and validated. This framework is characterized by: (i) the introduction of a new notion of trees, the so-called typed unranked labeled trees (tulab trees for short) in which each node receives one of three possible types (up, down or fix), and (ii) the definition of a new notion of tree automata, the so-called nested sibling tulab tree automata, able to enforce context-free style structural constraints on tulab tree languages. During their structural control process, such automata are using visibly pushdown languages of words [R. Alur and P. Madhusudan, Visibly pushdown languages, 36th ACM symposium on Theory of Computing, Chicago, USA (2004) 202-211] on their alphabet of states. We show that the resulting class NSTL of tulab tree languages recognized by nested sibling tulab tree automata is robust, $i.e.$ closed under Boolean operations and with decision procedures for the classical membership, emptiness and inclusion problems. We then give three characterizations of NSTL: a logical characterization by defining an adequate logic in which NSTL happens to coincide with the models of monadic second order sentences; the two other characterizations are using adequate encodings and map together languages of NSTL with some regular sets of 3-ary trees or with particular sets of binary trees.

Keywords: automata, logic, unranked trees, XML schemas

@article{ITA_2009__43_2_379_0, author = {Gire, Fran\c{c}oise and Talbot, Jean-Marc}, title = {Nested sibling tree automata}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {379--402}, publisher = {EDP-Sciences}, volume = {43}, number = {2}, year = {2009}, doi = {10.1051/ita/2009006}, zbl = {1171.68020}, mrnumber = {2512265}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita/2009006/} }

TY - JOUR AU - Gire, Françoise AU - Talbot, Jean-Marc TI - Nested sibling tree automata JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2009 DA - 2009/// SP - 379 EP - 402 VL - 43 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2009006/ UR - https://zbmath.org/?q=an%3A1171.68020 UR - https://www.ams.org/mathscinet-getitem?mr=2512265 UR - https://doi.org/10.1051/ita/2009006 DO - 10.1051/ita/2009006 LA - en ID - ITA_2009__43_2_379_0 ER -

%0 Journal Article %A Gire, Françoise %A Talbot, Jean-Marc %T Nested sibling tree automata %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 379-402 %V 43 %N 2 %I EDP-Sciences %U https://doi.org/10.1051/ita/2009006 %R 10.1051/ita/2009006 %G en %F ITA_2009__43_2_379_0

Gire, Françoise; Talbot, Jean-Marc. Nested sibling tree automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 2, pp. 379-402. doi : 10.1051/ita/2009006. http://www.numdam.org/articles/10.1051/ita/2009006/

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