RAIRO-Theor. Inf. Appl.
Volume 43, Number 2, April-June 2009
|Page(s)||379 - 402|
|Published online||12 March 2009|
Nested Sibling Tree Automata
Université de Paris I, Centre de Recherche en
Informatique Paris Cedex 13, France. email@example.com
2 Université de Provence, LIF Marseille France. firstname.lastname@example.org
Accepted: 19 January 2009
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.
Mathematics Subject Classification: 68Q45 / 68P15
Key words: Automata / logic / unranked trees / XML schemas.
© EDP Sciences, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.