  We present an exact pseudofermion action for hybrid Monte Carlo simulation
(HMC) of one-flavor domain-wall fermion (DWF), with the effective 4-dimensional
Dirac operator equal to the optimal rational approximation of the overlap-Dirac
operator with kernel $ H = c H_w (1 + d \gamma_5 H_w)^{-1} $, where $ c $ and $
d $ are constants. Using this exact pseudofermion action, we perform HMC of
one-flavor QCD, and compare its characteristics with the widely used rational
hybrid Monte Carlo algorithm (RHMC). Moreover, to demonstrate the practicality
of the exact one-flavor algorithm (EOFA), we perform the first dynamical
simulation of the (1+1)-flavors QCD with DWF.
