  We prove that when the equations are restricted to the principal part the
standard version of the BSSN formulation of the Einstein equations is
equivalent to the NOR formulation for any gauge, and that the KST formulation
is equivalent to NOR for a variety of gauges. We review a family of elliptic
gauge conditions and the implicit parabolic and hyperbolic drivers that can be
derived from them, and show how to make them symmetry-seeking. We investigate
the hyperbolicity of ADM, NOR and BSSN with implicit hyperbolic lapse and shift
drivers. We show that BSSN with the coordinate drivers used in recent "moving
puncture" binary black hole evolutions is ill-posed at large shifts, and
suggest how to make it strongly hyperbolic for arbitrary shifts. For ADM, NOR
and BSSN with elliptic and parabolic gauge conditions, which cannot be
hyperbolic, we investigate a necessary condition for well-posedness of the
initial-value problem.
