  We introduce the problem of temporal coverability for realizability and
synthesis. Namely, given a language of words that must be covered by a produced
system, how to automatically produce such a system. We consider the case of
coverability with no further specifications, where we have to show that the
nondeterminism of the produced system is sufficient to produce all the words
required in the output language. We show a counting argument on a deterministic
automaton representing the language to be covered that allows to produce such a
system. We then turn to the case of coverability with additional specification
and give a precondition for the existence of a system that produces all
required words and at the same time produces only computations satisfying the
additional correctness criterion. We combine our counting argument on the
deterministic automaton for the language to be covered with a ranking on the
deterministic B\"uchi automaton for the correctness criterion.
  One of the major issues with practical realizability is the interaction
between environment assumptions and system guarantees. In many cases, synthesis
produces systems that are vacuous and concentrate on forcing the environment to
falsify its assumptions instead of fulfilling their guarantees. Coverability
offers an alternative approach to tackle this problem.
