Algorithm 6. Synchronous product construction between $\mathcal{M}=⟨R{S}^M,NS{F}^M⟩$ and $\mathcal{A}=⟨Q,AP,\delta ,Q_0,\mathcal{F}⟩$.

1: procedure BUILDSYNCHPRODUCT(M, $\mathcal{A}$)

2:   // Build the MDD of the initial states.

3:   Z0 ← MDD()

4:   for each location q0 ∈ Q0: do

5:     for each edge $e=q_0\stackrel{a}{\to }q\mathrm{\prime }$ in δ: do

6:        Z0 ← Z0 ∪ AddLoc(SatM(a), q′)

7:     end for

8:   end for

9:   // Build the Next State Function M×D

10:  NSF ← M×D()

11:  for each edge $e=q\stackrel{a}{\to }q\mathrm{\prime }$ in δ: do

12:     nsf e ← AddLocX(NSFM ∩ (PSM × SatM(a)), q, q′)

13:    NSF ← NSF ∪ nsfe

14:  end for

15:  // $S_{\mathcal{F}}$: array of MDDs, one entry per accept. set Fi ∈ $\mathcal{F}$

16:  for each accepting set Fi ∈ $\mathcal{F}$: do

17:     ${\mathrm{M}\mathrm{D}\mathrm{D}}_{F_i}\leftarrow \cup \{edgeForVar(q)|\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{h}q\in F_i\}$

18:     $S_{\mathcal{F}}[i]\leftarrow \{{\mathrm{M}\mathrm{D}\mathrm{D}}_{F_i}\}$

19:  end for

20:  return $⟨Z_0,NSF,S_{\mathcal{F}}⟩$

21: end procedure