Zusammenfassung
In \cite{Andreka}, a large number of completeness results about variants
of discrete linear-time temporal logic are obtained. One of them is left
as an open problem:
the completeness of the logic of initially and next, for which a
deductive system is proposed. This simple logic is of practical
importance, since the proof of program invariants only require these
modalities.
We show here that the conjectured {\em medium completeness} of this
system indeed holds;
further, we show that deciding this entailment is PSPACE-complete, while
deciding validity is only coNP-complete.
