a modern C++ library for the manipulation of Boolean functions

3.2.18 Forcing some variables to be equivalent in a positive function
The algorithm expand_equivalent_vars can be used to perform efficiently the inverse
operation for the one presented in 3.2.15, that is conjuncting a Boolean function with the
equivalence conditions given by an equivalence relation, for the case when f ∈ Pos.
Given a ROBDD representing f and the equivalence relation L, we define the current
variable xc and the set of true leaders T ; the first is initialized to the smallest variable in
dom(L), while the second is initialized to ∅. Afterwards, we start from the root of the
ROBDD and follow these steps:
Step 1 If this node is 1 return the result of the application of the algorithm
make_equivalent_vars (presented in 3.2.10) on the same relation L, using the
same values for xc and T .
Step 2 If this node if 0 return 0.
Step 3 If xc is undefined (which means that we have already processed all variables in
dom(L)) return the current node.
Step 4 Let x be the variable by which this node is labeled. If x ≺ xc return the node
labeled with x and having the results of the recursive calls of this algorithm (with
the same values for xc and T ) on the true and false successors of the current node
as its true and false successors respectively.
Step 5 Let xn be the smallest variable in dom(L) that is greater than xc. If x = xc then
xc must be a leader for L, so we return the node labeled with xc, having the result
of the recursive application of this algorithm on the true successor of this node with
xn as the current variable and with T = T ∪ {xc} as its true successor and the result
of the recursive application of this algorithm on the false successor of this node with
xn as the current variable and with the same old value of T as its false successor.
Step 6 Otherwise, let xl = λL(xc). If xl = xc then xc is a leader for L so we return the
node labeled with xc, having the result of the recursive application of this algorithm
on this same node with xn as the current variable and with T = T ∪ {xc} as its
true successor and the result of the recursive application of this algorithm on this
same node with xn as the current variable and with the same old value of T as its
false successor.
Step 7 If xl ∈ T return the node labeled with xc, having the result of the recursive
application of this algorithm on this same node with xn as the current variable and
with the same value of T as its true successor and 0 as its false successor.
Step 8 Otherwise, return the node labeled with xc, having the result of the recursive
application of this algorithm on this same node with xn as the current variable and
with the same value of T as its false successor and 0 as its true successor.
3.2 ROBDD algorithms 29