Algorithm 4. CTL ${}^{\ast }$ model-checking algorithm.

1: procedure SatCTL ${}^{\ast }$(M, Ψ)

2: switch Ψ do

3:   case a ∈ AP: return {s ∈ SM | s |= a}

4:   case Ψ1 ∧ Ψ2:

5:     return SatCTL ${}^{\ast }$(Ψ1) ∩ SatCTL ${}^{\ast }$(Ψ2)

6:   case ⫬Ψ: return SM \ SatCTL ${}^{\ast }$(Ψ)

7:   case Eϕ: return Sat∃LTL(M, rewrite(ϕ))

8: end procedure