Abstract
We present a formalisation of the unified translation approach of
linear temporal logic (LTL) into ω-automata from [1]. This approach
decomposes LTL formulas into “simple” languages and allows
a clear separation of concerns: first, we formalise the purely logical
result yielding this decomposition; second, we instantiate this
generic theory to obtain a construction for deterministic
(state-based) Rabin automata (DRA). We extract from this particular
instantiation an executable tool translating LTL to DRAs. To the best
of our knowledge this is the first verified translation from LTL to
DRAs that is proven to be double exponential in the worst case which
asymptotically matches the known lower bound.
[1] Javier Esparza, Jan Kretínský, Salomon Sickert. One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata. LICS 2018