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

3.2.12 Shift renaming
The algorithm shift_rename takes an unsigned integer n and renames each variable vi in
a ROBDD to vi+n; it is implemented easily by renaming the root then calling recursively
on its true and false successors. Pseudo-code is given in Algorithm 10.
Require: a ROBDD node n and an offset s
function shift_rename(n, s)
if is_leaf(n) then
return n
else
return make_node x variable_index(n)+s, shift_rename(ntrue, s),
shift_rename(nfalse, s)
Algorithm 10: The shift_rename function
3.2.13 Renaming with respect to an equivalence relation
Suppose that we have a ROBDD n representing the Boolean function f and an equivalence
relation R and we want to rename each variable in n to its leader in R. This operation is
realized by the rename algorithm.
We start by defining the current variable xc and the set of true leaders T . The first is
initialized to x0, while the second is initialized to ∅. The algorithm starts from the root
of the ROBDD and proceeds as follows:
Step 1 If this node is 0 or 1 or it is labeled with a variable that is greater than the
greatest variable in dom(R), return this node.
Step 2 Let xi be the variable by which this node is labeled. If there exists the minimum
leader xl for R such that xc xl ≺ xi return the node that is labeled with xl, has
the result of the recursive application of this algorithm on this same node with xl+1
as the current variable and with T = T ∪ {xl} as its true successor and has the
result of the recursive application of this algorithm on this same node with xl+1 as
the current variable and with the same old value of T as its false successor.
Step 3 If xi /∈ dom(R) return the node that is labeled with xi and has the results of the
recursive applications of this algorithm on the true and false successors of this node
with xi+1 as the current variable and with the same value of T as its true and false
successors respectively.
Step 4 If λR(xi) = xi return the node that is labeled with xi, has the result of the
recursive application of this algorithm on the true successor of this node with xi+1
as the current variable and with T = T ∪ {xi} as its true successor and has the
result of the recursive application of this algorithm on the false successor of this
node with xi+1 as the current variable and with the same old value of T as its false
successor.
3.2 ROBDD algorithms 22