Huge lower bounds of weak logics for data words

I will show how to code very hard problems into the satisfiability of the linear temporal logic (LTL) equipped with one register to store and test data values from positions of a data word. I will show that this lower bound holds even when there only navigational modality is the Future. I will mention some of the consequences this entails for the satisfiability of some fragments of XPath over XML documents. Joint work with Luc Segoufin.