Translation of LTL to Omega Automata (2022-09-06 7.a)

Question

Do we need to take two variables (p and q) in this one as it's just G[a U B]? Can't we write just this?

G[q ↔ [φ U ψ]] ⇔ G[q ↔ ψ ∨ φ ∧ Xq]∧ GF[φ → q]



 

Answer 1

Yes, that can be improved. We can abbreviate the inner formula which is enough to obtain a safety automaton:

G[a WU b] = AE({p},1,p<->b|a&Xp,Gp)

That simplifies the entire exam problem, of course.