It remains to show how an OBDD for pre∃(X) and pre∀(X) can be computed,
given OBDDs BX for X and B→ for the transition relation →. First
we observe that pre∀ can be expressed in terms of complementation and
pre∃, as follows: pre∀(X) = S − pre∃(S − X), where we write S − Y for the
set of all s ∈ S which are not in Y . Therefore, we need only explain how to
compute the OBDD for pre∃(X) in terms of BX and B→. Now (6.4) suggests
that one should proceed as follows:
1. Rename the variables in BX to their primed versions; call the resulting OBDD
BX .
2. Compute the OBDD for exists(ˆx , apply(·,B→,BX )) using the apply and
exists algorithms
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