Algorithm 7. Implementation view of SAT∃LTL.

1: procedure SAT∃LTL(M, φ)

2:    $\mathcal{A}$ ← translate φ into a Büchi Automaton

3:    $⟨Z_0,NSF,S_{\mathcal{F}}⟩$ ← BUILDSYNCHPRODUCT(M, $\mathcal{A}$)

4:   S ← Saturate(Z0, NSF)

5:   K = (S, NSF ) is a Kripke model

6:   AS ← MDD()

7:   switch type( $\mathcal{A}$) do

8:      case weak:

9:       AS ← SATCTL $AS\leftarrow SATCTL(K,EFEG(S_{\mathcal{F}}[1]))$

10:     case terminal:

11:       AS ← SATCTL $AS\leftarrow SATCTL(K,EF(S_{\mathcal{F}}[1]))$

12:     case otherwise:

13:       AS ← SATEFAIR $AS\leftarrow {\mathrm{S}\mathrm{A}\mathrm{T}\mathrm{E}}_{\mathrm{F}\mathrm{A}\mathrm{I}\mathrm{R}}G(K,\mathbf{t}\mathbf{r}\mathbf{u}\mathbf{e},fair=S_{\mathcal{F}}):$

14:   Sat(∃φ) ← RemLoc(AS ∩ Z0)

15:   return Sat(∃φ)

16: end procedure