  We undertake a regularity analysis of the solutions to initial/boundary value
problems for the (third-order in time) Moore-Gibson-Thompson (MGT) equation.
The key to the present investigation is that the MGT equation falls within a
large class of systems with memory, with affine term depending on a parameter.
For this model equation a regularity theory is provided, which is of also
independent interest; it is shown in particular that the effect of boundary
data that are square integrable (in time and space) is the same displayed by
wave equations. Then, a general picture of the (interior) regularity of
solutions corresponding to homogeneous boundary conditions is specifically
derived for the MGT equation in various functional settings. This confirms the
gain of one unity in space regularity for the time derivative of the unknown, a
feature that sets the MGT equation apart from other PDE models for wave
propagation. The adopted perspective and method of proof enables us to attain
as well the (sharp) regularity of boundary traces.
