Depth efficient transformations of arithmetic into Boolean circuits

We present depth efficient transformations of arithmetic into boolean circuits. Any arithmetic circuit Cn over the integers can be converted to an O(d(n)·log*n) depth bounded boolean circuit, where d(n) is the depth of Cn. Furthermore, given any arithmetic circuit Cn over the integers with depth d(n) and f(n) bounded fan-in we can construct a boolean circuit simulating Cn within depth O(d(n)·logf(n)·(log*n−log*f(n))). The introduced transformations can be used to obtain very fast boolean circuits for several arithmetic problems, including the inversion of banded matrices.