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

The implementation is quite simple: we visit the ROBDD as usual. When we encounter
a node that is labeled with a leader for L the result is simply a node having the same label
and the results of the recursive calls on the original node’s successors as its successors,
otherwise one of the successors of the node must be 0 and we return the result of the
recursive call of the algorithm on the other node (thus projecting away this node). You
can find the pseudo-code in Algorithm 14.
Require: a ROBDD node n and an equivalence relation L
function squeeze_equivalent_vars(n, L)
if is_leaf(n) or max(dom(L)) ≺ nvar then
return n
else
if nvar /∈ dom(L) or λL(nvar) = nvar then
return make_node nvar, squeeze_equivalent_vars(ntrue, L),
squeeze_equivalent_vars(nfalse, L)
else
if ntrue = 0 then
return squeeze_equivalent_vars(nfalse, L)
else
return squeeze_equivalent_vars(ntrue, L)
Algorithm 14: The squeeze_equivalent_vars function
3.2.16 Combined search and elimination of entailed and disentailed
variables
Suppose that we have a ROBDD n for Boolean function f and we know some (but
not necessarily all) entailed variables for f, i.e. we know E ⊂ true(f). The algorithm
elim_search_true_vars can be used to eliminate all entailed variables in E from n
while adding some other unknown entailed variables for f to E. Repeated application of
this algorithm on the same ROBDD is guaranteed to reach a fixpoint where E contains
all and only the entailed variables for f and n does not have any entailed variable.
Algorithm elim_search_false_vars is the analogous for disentailed variables. Pseudocodes
for both can be found in Algorithm 15 and Algorithm 16 (notice that they return a
pair (n, S)).
3.2.17 Forcing a set of variables to true or false
Given a ROBDD n representing the Boolean function f and a finite set of variables
S = x1, x2, . . . , xn, the algorithm and_vs_true computes the ROBDD representing the
Boolean function f ∧ x1 ∧ x2 ∧ . . . ∧ xn (the algorithm and_vs_false which computes
f ∧ x1 ∧ x2 ∧ . . . ∧ xn is very similar to this one). We traverse the ROBDD starting from
the root node , initialize the current variable xc = x1, and apply the following steps:
3.2 ROBDD algorithms 25