Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t 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 straightline regular tree grammar associated to the given dag, or along complete sibling chains in this grammar. Any given 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 suitably labeled under the runs of such automata.