In a first part of this work, tree/dag automata are defined as extensions of (unranked) tree automata which can run indifferently on trees or dags; they can thus serve as tools for analyzing or querying any semi-structured document, whether or not given in a compressed format. In a second part of the work, we present a method for evaluating positive unary queries, expressed in terms of Core XPath axes, on any dag t, representing an XML document possibly given in a compressed form; the evaluation is done directly on t, without unfolding it into a tree. To each Core XPath query of a certain basic type, we associate a word automaton; these automata run on the graph of dependency between the non-terminals of the minimal straightline regular tree grammar associated to the given dag t, or along complete sibling chains in this grammar. Any given positive Core XPath query can be decomposed into queries of the basic type, and the answer to the query, on the dag t, can then be expressed as a sub-dag of t whose nodes are suitably labeled under the runs of such automata.