  The study of node selection query languages for (finite) trees has been a
major topic in the recent research on query languages for Web documents. On one
hand, there has been an extensive study of XPath and its various extensions. On
the other hand, query languages based on classical logics, such as first-order
logic (FO) or Monadic Second-Order Logic (MSO), have been considered. Results
in this area typically relate an XPath-based language to a classical logic.
What has yet to emerge is an XPath-related language that is as expressive as
MSO, and at the same time enjoys the computational properties of XPath, which
are linear time query evaluation and exponential time query-containment test.
In this paper we propose muXPath, which is the alternation-free fragment of
XPath extended with fixpoint operators. Using two-way alternating automata, we
show that this language does combine desired expressiveness and computational
properties, placing it as an attractive candidate for the definite
node-selection query language for trees.
