  We study theoretically edge transport of a fractional quantum Hall liquid, in
the presence of a quantum dot inside the Hall bar with well controlled electron
density and Landau level filling factor \nu, and show that such transport
studies can help reveal the nature of the fractional quantum Hall liquid. In
our first example we study the \nu=1/3 and \nu=2/3 liquids in the presence of a
\nu=1 quantum dot. When the quantum dot becomes large, its edge states join
those of the Hall bar to reconstruct the edge states configuration. Taking
randomness around the edges into account, we find that in the
disorder-irrelevant phase the two-terminal conductance of the original \nu=1/3
system vanishes at zero temperature, while that of the \nu=2/3 case remains
finite. This distinction is rooted in the fact that the \nu=2/3 state is built
upon the \nu=1 state. In the disorder-dominated phase, the two-terminal
conductance of \nu=1/3 system is (1/5)\frac{e^2}{h} and that of \nu=2/3 system
is (1/2)\frac{e^2}{h}. We further apply the same idea to the \nu=5/2 system
which realizes either the Pfaffian or the anti-Pfaffian states. In this case we
study the edge transport in the presence of a central \nu=3 quantum dot. If the
quantum dot is large enough for its edge states joining those of the Hall bar,
in the disorder-irrelevant phase the total two-terminal conductance in the
Pfaffian case is G^{Pf}_{tot}\rightarrow 2 \frac{e^2}{h} while that of
anti-Pfaffian case is higher but not universal, G^{aPf}_{tot}> 2 \frac{e^2}{h}.
This difference can be used to determine which one of these two states is
realized at \nu=5/2. In the disorder-dominated phase, however, the total
two-terminal conductances in these two systems are exactly the same,
G^{Pf/aPf}_{tot}=(7/3)\frac{e^2}{h}.
