Conference Proceeding

XML Schema, Tree Logic and Sheaves Automata.

Applicable Algebra in Engineering Communication and Computing (Impact Factor: 0.76). 01/2003; DOI:10.1007/3-540-44881-0_18 In proceeding of: Rewriting Techniques and Applications, 14th International Conference, RTA 2003, Valencia, Spain, June 9-11, 2003, Proceedings
Source: DBLP

ABSTRACT XML documents may be roughly described as unranked, ordered trees and it is therefore natural to use tree automata to process or validate them. This idea has already been successfully applied in the context of Document Type Defi- nition (DTD), the simplest standard for defining document va lidity, but additional work is needed to take into account XML Schema, a more advanced standard, for which regular tree automata are not satisfactory. In thi s paper, we introduce Sheaves Logic (SL), a new tree logic that extends the syntax of the — recursion- free fragment of — W3C XML Schema Definition Language (WXS). Then we define a new class of automata for unranked trees that provide s decision proce- dures for the basic questions about SL: model-checking; satisfiability; entailment. The same class of automata is also used to answer basic questions about WXS, in- cluding recursive schemas: decidability of type-checking documents; testing the emptiness of schemas; testing that a schema subsumes another one.

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    ABSTRACT: We define tree automata with global constraints (TAGC), generalizing the well-known class of tree automata with global equality and disequality constraints (14) (TAGED). TAGC can test for equality and disequality between sub- terms whose positions are defined by the states reached dur- ing a computation. In particular, TAGC can check that all the subterms reaching a given state are distinct. This con- straint is related to monadic key constraints for XML docu- ments, meaning that every two distinct positions of a given type have different values. We prove decidability of the emptiness problem for TAGC. This solves, in particular, the open question of de- cidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for count - ing the number of occurrences of some state or the number of different subterms reaching some state during a compu- tation. We also allow local equality and disequality tests between sibling positions and the extension to unranked ordered trees. As a consequence of our results for TAGC, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality.
    Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010, 11-14 July 2010, Edinburgh, United Kingdom; 01/2010
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    ABSTRACT: We present algorithms for testing language inclusion L(A) ⊆ L(B) between tree automata in time O(|A| · |B|) where B is deterministic (bottom-up or top-down). We extend our algorithms for testing inclusion of automata for unranked trees A in deterministic DTDs or deterministic EDTDs with re- strained competition D in time O(|A| · |Σ| · |D|). Previous algorithms were less efficient or less general.
    01/2009;
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    ABSTRACT: We introduce the extended modal logic EML with regularity constraints and full Presburger constraints on the number of children that generalize graded modali- ties, also known as number restrictions in description logics. We show that EML satisfiability is only pspace-complete by designing a Ladner-like algorithm. This extends a well-known and non-trivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we provide a logarithmic space reduction from a variant of Sheaves logic SL into EML that allows us to establish that its satisfiability problem is also pspace-complete, significantly improving the best known upper bound.
    J. Applied Logic. 01/2010; 8:233-252.

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