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As the high-density nuclear equation of state (EOS) is not very well constrained, we suggest that the structural properties from the finite systems can be used to extract a more accurate constraint. By including the stran-geness degrees of freedom, the hyperon or anti-kaon, the finite systems can then have a rather high-density core which is relevant to the nuclear EOS at high densities directly. It is found that the density dependence of the symmetry energy is sensitive to the properties of multi-Λ hypeuclei, while the high-density EOS of symmetric matter correlates sensitively to the properties of kaonic nuclei.