Asymptotic Growth

In describing the size and depth of a circuit, the terms ``logarithmic'', ``linear'', ``quadratic'', ``polynomial'', and ``exponential'' are often used. These terms are used to describe bounds on the growth of some function (usually the size of output or time to generate it) within a constant factor.

Name	Proportional to
logarithmic	$\lg n$
linear	$n$
quadratic	$n^2$
polynomial	$n^k$ for some fixed $k$
exponential	$c^n$ for some fixed $c$

For example, a function described as linear will generally double in size when its input doubles. These ideas will be formalized later as ``big-O'' notation when you take an algorithms class.