Integer multiplication as one of the basic arithmetic functions has
been in the focus of several complexity  theoretical investigations.
Ordered binary decision diagrams (OBDDs) are one of the most common
dynamic data structures for boolean functions.  
Analyzing the limits of symbolic graph algorithms for the reachability 
problem Sawitzki (2006) has presented the first exponential lower bound
on the pi-OBDD size for the most significant bit of integer multiplication 
according to one predefined variable order pi. Since the choice of the 
variable order is a main issue to obtain OBDDs of small size, the 
investigation is continued. As a result a new upper bound method and the 
first non-trivial upper bound on the size of OBDDs according to an arbitrary 
variable order is presented. Furthermore, Sawitzki's lower bound is 
improved.

Moreover, it is shown that the OBDD complexity of the most significant bit 
is exponential answering an open question posed by Wegener (2000).