  Quantitative extensions of temporal logics have recently attracted
significant attention. In this work, we study frequency LTL (fLTL), an
extension of LTL which allows to speak about frequencies of events along an
execution. Such an extension is particularly useful for probabilistic systems
that often cannot fulfil strict qualitative guarantees on the behaviour. It has
been recently shown that controller synthesis for Markov decision processes and
fLTL is decidable when all the bounds on frequencies are 1. As a step towards a
complete quantitative solution, we show that the problem is decidable for the
fragment fLTL$\setminus$GU, where U does not occur in the scope of G (but still
F can). Our solution is based on a novel translation of such quantitative
formulae into equivalent deterministic automata.
