Larger Lower Bounds on the OBDD Complexity of Integer Multiplication

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. Only recently it has been shown that the OBDD complexity of the most, significant bit of integer multiplication is exponential, answering an open question posed by Wegener (2000). In this paper a larger lower bound is presented, using a simpler proof. Moreover, the best known lower bound on the OBDD complexity for the so-called graph of integer multiplication is improved.