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

computed normally and an hash entry corresponding to the performed computation is
added. Since we perform at most one recursive call for each pair of nodes and provided
that our implementation of hash tables is good enough to bring the average cost of each
recursive valuation to a constant value, the worst case complexity of the algorithm is in
the order of nm, where n and m are the number of nodes in the first and the second
ROBDD respectively.
The implementation of operators with more than two arguments can be easily extended
from this one.
2.3.2 Implementation of the restriction operation
Given a ROBDD representing the Boolean function f, v ∈ Vars and b ∈ {0, 1}, we can
compute f[b/x] with a recursive procedure starting from the root of the ROBDD: each
recursive call considers one node of the argument and returns one node of the resulting
ROBDD. The base case is when the considered node is labeled with v: here we must
simply return its true successor if b = 1 or its false successor if b = 0. For the recursive
case we simply make recursive calls on both successors. The reduction of the result and
the avoidance of multiple recursive calls can be guaranteed by using the usual techniques,
with the obvious exception that the keys of the hash table that is used to avoid multiple
recursive calls are composed by a single pointer.
The techniques described in this chapter can be used to implement most operations on
Boolean functions, although CORAL utilizes a few other tweaks which will be presented
in the next two chapters.
2.3 Operations on ROBDDs 10