  We give improved and almost optimal testers for several classes of Boolean
functions on $n$ inputs that have concise representation in the uniform and
distribution-free model. Classes, such as $k$-junta, $k$-linear functions,
$s$-term DNF, $s$-term monotone DNF, $r$-DNF, decision list, $r$-decision list,
size-$s$ decision tree, size-$s$ Boolean formula, size-$s$ branching programs,
$s$-sparse polynomials over the binary field and function with Fourier degree
at most $d$. The method can be extended to several other classes of functions
over any domain that can be approximated by functions that have a small number
of relevant variables.
