  Freeze LTL is a temporal logic with registers that is suitable for specifying
properties of data words. In this paper we study the model checking problem for
Freeze LTL on one-counter automata. This problem is known to be undecidable in
general and PSPACE-complete for the special case of deterministic one-counter
automata. Several years ago, Demri and Sangnier investigated the model checking
problem for the flat fragment of Freeze LTL on several classes of counter
automata and posed the decidability of model checking flat Freeze LTL on
one-counter automata as an open problem. In this paper we resolve this problem
positively, utilising a known reduction to a reachability problem on
one-counter automata with parameterised equality and disequality tests. Our
main technical contribution is to show decidability of the latter problem by
translation to Presburger arithmetic.
