  The Kugo-Ojima color confinement criterion, which is based on the BRST
symmetry of the continuum QCD is numerically tested by the lattice Landau gauge
simulation. We first discuss the Gribov copy problem and the BRST symmetry on
the lattice. The lattice Landau gauge can be formulated with options of the
gauge field definition, U(link)-linear type or log U type. The Kugo-Ojima
parameter u^a_b which is expected to be -1^a_b in the continuum theory is found
to be -0.7*1^a_b in the strong coupling region, and the magnitude is a little
less in the weak coupling region in log U type simulation. Those values are
weakened even further in U-linear type. The horizon function defined by
Zwanziger is evaluated in both types of gauge field and compared. The horizon
function in the log U version is larger than the other, but in the weak
coupling region, the expectation value of the horizon function is suggested to
be zero or negative.
