I am trying to figure out difference between fully- and quasi-reduced BDDs. I have read a lot of material but still it is not very clear. As I am trying to figure out the quasi reduced version for union between two BDDs. The algorithm for union between two fully-reduced BDDs is
bdd Union(bdd p, bdd q)
//fully-reduced version
local bdd r;
1 if p=0 or q=1 then return q;
2 if q=0 or p=1 then return p;
3 if p=q then return p;
4 if Cachecontainsentry⟨UnionCODE,{p,q}:r⟩ then return r;
5 if p.lvl = q.lvl then
6 r ← UniqueTableInsert(p.lvl, Union(p[0], q[0]), Union(p[1], q[1]));
7 else if p.lvl > q.lvl then
8 r ← UniqueTableInsert(p.lvl, Union(p[0], q), Union(p[1], q));
9 else since p.lvl < q.lvl then
10 r ← UniqueTableInsert(q.lvl, Union(p, q[0]), Union(p, q[1]));
11 enter⟨UnionCODE,{p,q}:r⟩inCache;
12 return r;
I have read the paper Binary decision diagrams in theory and practice by Rolf Drechsler, Detlef Sieling for basics of BDD, and Data Representation and Efficient Solution: A Decision Diagram Approach by Gianfranco Ciardo for quasi-reduced and fully reduced definitions. Then I read more papers with more or less same description of quasi- and fully-reduced BDDs. In the former paper I mentioned the authors talk about reduced BDDs, I am not clear whether these BDDs are fully reduced. Quasi-reduced BDDs has no variable skipping so how come they are reduced when they have redundant nodes. I am pretty confused between BDD, quasi-reduced BDD and fully-reduced BDD. Yes, I am trying to find the difference between union algorithm for quasi-reduced and fully-reduced, for this I need to look at the quasi-reduced version of union algorithm.
I figured out an algorithm for union of two quasi reduced BDDs p and q resulting in r.
bdd Union(bdd p, bdd q)
local bdd r;
1 if p=0 or q=1 then return q;
2 if q=0 or p=1 then return p;
3 if p=q then return p;
4 if Cachecontainsentry⟨UnionCODE,{p,q}:r⟩ then return r;
//p.lvl = q.lvl in case of quasi reduced BDDs
5 r ← UniqueTableInsert(p.lvl, Union(p[0], q[0]), Union(p[1], q[1]));
6 enter⟨UnionCODE,{p,q}:r⟩ in Cache;
7 return r;
Since there is no variable skipping, p.lvl is always equal to q.lvl. I have a question about this algorithm.
If I want to implement Xor or Xnor for quasi-reduced BDDs, can it be done the same way as union or should I implement the expression pq' + p'q where q' = !q.
