Relations Among Parallel and Sequential Computation Models

This paper relates uniform small-depth circuit families as a parallel computation model with the complexity of polynomial time Turing machines. Among the consequences we obtain are: (a) a collapse of two circuit classes is equivalent to a relativizable collapse of the two corresponding polynomial time classes; and (b) a collapse of uniformity conditions for small depth circuits is equivalent to a related absolute (i.e., unrelativized) collapse in the polynomial time world.