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

3.2.19 Exotic operators
CORAL also provides a few more specific ROBDD algorithms for the purpose of building
(efficiently) some ROBDDs representing particular classes of Boolean functions that are
often encountered in groundness analysis.
Functions of type v =⇒ v1 ∧ v2 ∧ . . . ∧ vn
ROBDDs for this class of functions are built by the if_conj algorithm, which takes v
and the set of variables V =
v1, v2, . . . vn , v /∈ V as its arguments. If all variables in V
are greater than v in the ordering the task is trivial, as the result is simply a ROBDD
whose root is labeled by v, has 1 as its false successor and has the ROBDD representing
v1 ∧ v2 ∧ . . . ∧ vn as its true successor: that’s why we start by considering only the grater
variables and building the ROBDD for them. The smaller variables are handled later, as
you can see in Algorithm 19.
Require: a variable v and a set of variables V
function if_conj(v, V )
nv = and_vs_true 1, x ∈ V . v ≺ x
nv = make_node v, nv, 1
S = x ∈ V . x ≺ v
if S = ∅ then
return nv
else
fv = make_node v, 0, 1
curr = prev = nv
while S = ∅ do
m = max(S)
curr = make_node m, prev, fv
prev = curr
S = S \ m
return curr
Functions of type v ⇐⇒ v1 ∧ v2 ∧ . . . ∧ vn
Algorithm 19: The if_conj function.
ROBDDs for this class of functions are built by the iff_conj algorithm, which takes
v and the set of variables V =
v1, v2, . . . vn , v /∈ V as its arguments. As for if_conj,
the construction is trivial if all variables in V are greater than v in the ordering, as the
result is simply a ROBDD whose root is labeled by v, has the ROBDD representing
¬v1∨¬v2∨. . .∨¬nn as its false successor and has the ROBDD representing v1∧v2∧. . .∧vn
as its true successor: that’s why, as for if_conj, we start by considering only the greater
variables and handle the smaller ones later. Pseudo-code is given in Algorithm 20.
3.2 ROBDD algorithms 30