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Abstract
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Introduction
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Monadic Datalog Over Trees
Definition 5.3 (Monadic Datalog Encoding)
References
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Computer Science
Database Systems

Monadic queries over tree-structured data

Profile image of Georg GottlobGeorg Gottlob

Proceedings 17th Annual IEEE Symposium on Logic in Computer Science

https://doi.org/10.1109/LICS.2002.1029828
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Abstract

Monadic query languages over trees currently receive considerable interest in the database community, as the problem of selecting nodes from a tree is the most basic and widespread database query problem in the context of XML. Partly a survey of recent work done by the authors and their group on logical query languages for this problem and their expressiveness, this paper provides a number of new results related to the complexity of such languages over so-called axis relations (such as "child" or "descendant") which are motivated by their presence in the XPath standard or by their utility for data extraction (wrapping).

Figures (2)
As a consequence of the previous theorem, we have In our graphical notation, the translation is
As a consequence of the previous theorem, we have In our graphical notation, the translation is
At the right, we show a mapping @ obtained by traversing the tree depth-first and always adding the first encounter of each variable to 6. Clearly, 6 is a satisfaction for our query. Example 8.3 Consider the query shown below on the left (all binary atoms are, say, of the form child*). Moreover, assume that for each variable x;, the query contains a unary atom label,., (x;). Below, in the center, We show a data tree and the labels the nodes are assigned. It is easy to verify that the Elimination Algorithm returns 1; € O(n) exactly if nis labeled x;.
At the right, we show a mapping @ obtained by traversing the tree depth-first and always adding the first encounter of each variable to 6. Clearly, 6 is a satisfaction for our query. Example 8.3 Consider the query shown below on the left (all binary atoms are, say, of the form child*). Moreover, assume that for each variable x;, the query contains a unary atom label,., (x;). Below, in the center, We show a data tree and the labels the nodes are assigned. It is easy to verify that the Elimination Algorithm returns 1; € O(n) exactly if nis labeled x;.

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