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

2 Reduced Ordered Binary Decision
Diagrams
2.1 Definition
2.1.1 ROBDD definition
Reduced Ordered Binary Decision Diagrams (ROBDDs), first introduced by Randal
E. Bryant in [Bry86] along with the basic algorithms that manipulate them, are the
fundamental data structure used by CORAL to represent Boolean functions. A ROBDD
is a rooted, directed, and acyclic graph where leaf nodes are either 0 or 1 (the terminal
nodes) and each non-leaf node n is labeled with a Boolean variable nvar ∈ Vars on which
the represented Boolean function depends (nvar ∈ vars(f)). Each non-leaf node has two
successors nfalse and ntrue, called the false successor and the true successor respectively.
Both successors can be either a leaf node or a non-leaf node labeled with a variable that
is greater than nvar (this explains the Ordered part of the name). Finally, no duplicate
nodes must be present (this explains the Reduced part of the name). As Bryant himself
showed, it is possible to transform any Ordered Binary Decision Diagram into a ROBDD
by applying a few simple reduction rules:
Remove duplicate terminal nodes: Keep no more than one copy of the terminal nodes
0 and 1 and redirect all edges that were directed towards the removed duplicates to
the remaining copies.
Remove duplicate non-terminal nodes: If two or more non-terminal nodes are labeled
with the same variable and share the same true and false successors, keep only one
copy and redirect all edges that were directed towards the removed duplicates to
the remaining copy.
Remove nodes having a unique successor: Remove all nodes that have their true successor
equal to their false successor and redirect all edges that were directed towards
them to their successor.
The rules must be applied repeatedly until a fixpoint is reached, as applying one rule
may lead to further reduction possibilities for the others. We now give a formal definition
for ROBDDs:
Definition 5. (ROBDDs.) If N is the set of nodes of a ROBDD then N satisfies
N ⊆ {0, 1} ∪ Vars × N × N.