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

We have four terminal cases (note that there could be more or less: this choice is the
result of statistical analysis):
If i = 1 the result is t.
If i = 0 the result is e.
If t = 1 and e = 0 the result is i.
If t = e the result is t.
The implementation of operators with more than two arguments can be easily extended
from the implementation of a generic binary operator, the main differences being that
the splitting is performed on three nodes on each recursive call and the hash table used
to avoid duplicate recursive calls uses a triple of ROBDD pointers as its key instead of a
couple. Pseudo-code for this algorithm can be found in Algorithm 3.
3.2.6 Specializations of if/then/else
CORAL also provides some specializations of the ite operator, the most important being
var_ite and gen_var_ite; their purpose is to provide a more efficient implementation
of ite for some particular cases, which will occur in particular during the algorithm for
the elimination of entailed variables that will be presented later.
For example, gen_var_ite(i, t, e) implements the particular case when i is a
ROBDD whose root has 1 and 0 as its direct true and false successors respectively.
gen_var_ite_g and gen_var_ite_h are further specializations of gen_var_ite: the
first is used when we know that the root of i is labeled with a variable that is smaller
than the one which labels the root of t, while the second is used when we know that the
root of i is labeled with a variable that is smaller than the one which labels the root of e.
var_ite(i, t, e) and its further specializations var_ite_g and var_ite_h are
analogous, but we add the hypothesis that the variable which labels the root of i does
not occour in t and e.
Here’s the list of all cases considered in the implementation of gen_var_ite(f, g, h).
Further informations, along with a correctness proof, can be found in [BS98]. For the
sole purpose of writing these cases more simply, we consider 0var and 1var to be special
variables that are greater than all other variables.
Case 1 If fvar = gvar = hvar,
return make_node
fvar, gtrue, htrue .
Case 2 If fvar < gvar < hvar or fvar < gvar = hvar or fvar < hvar < gvar,
return make_node fvar, g, h .
Case 3 If fvar = gvar < hvar,
return make_node fvar, gtrue, h .
3.2 ROBDD algorithms 15