Algorithm 1. Check LTL m_init |= Aφ as: $\mathrm{\forall }\pi \in {\mathcal{P}}_M^{\mathrm{\infty }}(m_{init})$: π|= φ.

1: procedure check∀LTL(M, φ)

2:  φ′← ⫬φ

3:   $\mathcal{A}$ ← translate φ′ into a Generalized Büchi Automaton

4:   $\mathcal{A}$ ← BA of the Kripke model M(RG)

5:   $\mathcal{M}$ ← synchronized product of $\mathcal{A}$ and $\mathcal{A}$

6:  if ℒ ( $\mathcal{M}\otimes \mathcal{A}$) is empty then return true

7:  else return false

8:  end if

9: end procedure