# 19.2 SafeLTL

An $ω$-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?