  Uncertainties on central mixing in main sequence (MS) and core He-burning
(He-B) phases affect key predictions of stellar evolution such as late
evolutionary phases, chemical enrichment, ages etc. We propose a test of the
extension of extra-mixing in two relevant evolutionary phases based on period
spacing Delta_P of solar-like oscillating giants. From stellar models and their
corresponding adiabatic frequencies (respectively computed with ATON and LOSC
codes) we provide the first predictions of the observable Delta_P for stars in
the red giant branch (RGB) and in the red clump (RC). We find: i) a clear
correlation between Delta_P and the mass of the helium core (M_He); the latter
in intermediate-mass stars depends on the MS overshooting, hence it can be used
to set constraints on extra mixing during MS when coupled with chemical
composition; ii) a linear dependence of the average value of the asymptotic
period spacing (<Delta_P>_a) during the He-B phase on the size of the
convective core. A first comparison with the inferred asymptotic period spacing
for Kepler RC stars suggests the need for extra mixing also during this phase,
as evinced from other observational facts.
