Bounds on the OBDD-size of integer multiplication via universal hashing

Bryant [5] has shown that any OBDD for the function MULn−1,n, i.e. the middle bit of the n-bit multiplication, requires at least 2n/8 nodes. In this paper a stronger lower bound of essentially 2n/2/61 is proven by a new technique, using a universal family of hash functions. As a consequence, one cannot hope anymore to verify e.g. 128-bit multiplication circuits using OBDD-techniques because the representation of the middle bit of such a multiplier requires more than 3 · 1017 OBDD-nodes. Further, a first non-trivial upper bound of 7/3 · 24n/3 for the OBDD-size of MULn−1,n is provided.