Heuristics for estimating the efficiency of Reduced Ordered Binary Decision Diagrams? Reduced Ordered Binary Decision Diagrams (ROBDD) are an efficient data structure for representing boolean functions of multiple variables $f(x_1,x_2,...,x_n)$. I would like to get an intuition for how efficient they are.

For instance, for data compression, we know that data with low entropy (some symbols appearing more often than other, many repetitions) can be compressed very well while completely random data cannot be compressed.


  Is there an analogous intuition for estimating how efficiently ROBDDs can represent a given boolean formula?


For example, I have heard that multiplication of $n$-bit numbers cannot be represented efficiently, the minimum ROBDD size is exponential in $n$. Do you know of an intuitive argument that explains why this is the case?

Related question: intuition about efficiency of BDDs that calculate numbers (multiple terminal BDDs, etc.)
There is a relation between the width of an OBDD for a function $f$ and the communication complexity of a one-way communication protocol for the best-case partition of variables for $f$ (see E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997).

This is a powerful tool for proving exponential size OBDDs for various functions (together with coauthors, we used this method for proving that $\epsilon$-bipartiteness is hard for OBDDs, see here). 
Basically, if there exists an OBDD of width at most $w$ that solves $f$, then $\kappa_{best}(f) \leq \log w$.
I think this is more intuitive to think in terms of communication complexity rather than OBDD.