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

Case 4 If fvar = hvar < gvar,
return make_node
fvar, g, hfalse .
Case 5 If gvar < fvar < hvar,
return make_node gvar, gen_var_ite_h(f, gtrue, h), gen_var_ite_h(f, gfalse, h) .
Case 6 If gvar < fvar = hvar or gvar < hvar < fvar,
return make_node gvar, gen_var_ite(f, gtrue, h), gen_var_ite(f, gfalse, h) .
Case 7 If gvar = hvar < fvar,
return make_node gvar, gen_var_ite(f, gtrue, htrue), gen_var_ite(f, gfalse, hfalse) .
Case 8 If hvar < fvar < gvar,
return make_node hvar, gen_var_ite_g(f, g, htrue), gen_var_ite_g(f, g, hfalse) .
Case 9 If hvar < fvar = gvar or hvar < gvar < fvar,
return make_node hvar, gen_var_ite(f, g, htrue), gen_var_ite(f, g, hfalse) .
The set of cases for var_ite is a strict subset of these cases, obtained by removing
the ones where fvar = gvar or fvar = hvar and replacing all calls to gen_var_ite,
gen_var_ite_h and gen_var_ite_g with calls to var_ite, var_ite_h and var_ite_g
respectively.
3.2.7 Variables on which a Boolean function depends
The algorithm vars which takes a ROBDD representing the Boolean function f and
returns vars(f) can be easily implemented by visiting the ROBDD and collecting the
variables that label the nodes. This algorithm is one of the few ROBDD algorithms in
CORAL for which no caching is provided. Pseudo-code is given in Algorithm 4.
Require: a ROBDD node n
function vars(n)
if n = 0 or n = 1 then
return ∅
else
return
nvar ∪vars(ntrue) ∪ vars(nfalse)
Algorithm 4: The vars function
3.2.8 Entailed and disentailed variables
The algorithms entailed_vars and disentailed_vars (and their counterparts
entailed_vars_no_cache and disentailed_vars_no_cache, which don’t use caching)
are used to compute true(f) and false(f). In order to compute the set of all entailed
variables in a ROBDD, we start from its root node and follow these steps (the algorithm
that looks for disentailed variables is very similar):
3.2 ROBDD algorithms 17