  The evolution of stars born with a convective core is highly dependent on the
efficiency and extent of near core mixing processes, which effectively
increases both the core mass and main-sequence lifetime. We investigate to what
extent gravity-mode period spacings in slowly pulsating B-type stars observed
by the Kepler mission can be used to constrain both the shape and extent of
convective core overshoot and additional mixing in the radiative envelope. We
compute grids of 1D stellar structure and evolution models for two different
shapes of convective core overshooting and three shapes of radiative envelope
mixing. The models in these grids are compared to a set of benchmark models to
evaluate their capability of mimicking the dipole prograde g-modes of the
benchmark models. Through our model comparisons we find that at a central
hydrogen content of Xc = 0.5, dipole prograde g-modes in the period range 0.8-3
d are capable of differentiating between step and exponential diffusive
overshooting. This ability disappears towards the terminal age main-sequence at
Xc = 0.1. Furthermore, the g-modes behave the same for the three different
shapes of radiative envelope mixing considered. However, a constant envelope
mixing requires a diffusion coefficient near the convective core five times
higher than chemical mixing from internal gravity waves to obtain a surface
nitrogen excess of about 0.5 dex within the main-sequence lifetime. Within
estimated frequency errors of the Kepler mission, the ability of g-modes to
distinguish between step and exponential diffusive overshooting depends on the
evolutionary stage. Combining information from the average period spacing and
observed surface abundances, notably nitrogen, could potentially be used to
constrain the shape of mixing in the radiative envelope of massive stars.
