SafeLTL

An $\omega$-word language $L\subseteq \Sigma^\omega$ is a safety language if for all $w\not \in L$ there is a prefix $v\in \Sigma^*$ of $w$ such that for all $u\in \Sigma^\omega$, $vu\not \in L$. safeLTL is the fragment of negation normal form LTL without Until nor Finally. SafeLTL captures exactly LTL expressible safety properties. However, to go from an LTL formula describing a safety property to an equivalent safeLTL formula, the best known translation seems to go via a deterministic safety automaton and then back to LTL, incurring a triple-exponential blow-up on the way. Open problem: Is there a (more) concise translation from LTL to safeLTL? Are there safety properties that are exponentially more concisely expressible in LTL than safeLTL?