  We introduce the problem of variable-length source resolvability, where a
given target probability distribution is approximated by encoding a
variable-length uniform random number, and the asymptotically minimum average
length rate of the uniform random numbers, called the (variable-length)
resolvability, is investigated. We first analyze the variable-length
resolvability with the variational distance as an approximation measure. Next,
we investigate the case under the divergence as an approximation measure. When
the asymptotically exact approximation is required, it is shown that the
resolvability under the two kinds of approximation measures coincides. We then
extend the analysis to the case of channel resolvability, where the target
distribution is the output distribution via a general channel due to the fixed
general source as an input. The obtained characterization of the channel
resolvability is fully general in the sense that when the channel is just the
identity mapping, the characterization reduces to the general formula for the
source resolvability. We also analyze the second-order variable-length
resolvability.
