An exponential lower bound on the size of a binary moment diagram representing integer division.
A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0,1}(n) --> Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions with polynomial numbers of vertices. Lower bounds for division, however, had not been investigated. In this paper, we show an exponential lower bound on the number of vertices of a multiplicative binary moment diagram representing a quotient function or a remainder function.
lower bound binary moment diagram division