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The half-skyrmions that appear in dense baryonic matter when skyrmions areput on crystals modify drastically hadron properties in dense medium and affectstrongly the nuclear tensor forces, thereby influencing the equation of state(EoS) of dense nuclear and asymmetric nuclear matter. The matter comprised ofhalf skyrmions has vanishing quark condensate but non-vanishing pion decayconstant and could be interpreted as a hadronic dual of strong-coupled quarkmatter. We infer from this observation combined with certain predictions ofhidden local symmetry in low-energy hadronic interactionsa a set of new scalinglaws -- called "new-BR" -- for the parameters in nuclear effective field theorycontrolled by renormalization-group flow. They are subjected to the EoS ofsymmetric and asymmetric nuclear matter, and are then applied to nuclearsymmetry energies and properties of compact stars. The changeover from theskyrmion matter to a half-skyrmion matter that takes place after the cross-overdensity $n_{1/2}$ provides a simple and natural field theoretic explanation forthe change of the EoS from soft to stiff at a density above that of nuclearmatter required for compact stars as massive as $\sim 2.4M_\odot$. Cross-overdensity in the range $1.5n_0 \lsim n_{1/2} \lsim 2.0 n_0$ has been employed,and the possible skyrmion half-skyrmion coexistence {or cross-over} near$n_{1/2}$ is discussed. The novel structure of {the tensor forces and} the EoSobtained with the new-BR scaling is relevant for neutron-rich nuclei andcompact star matter and could be studied in RIB (rare isotope beam) machines.

Half-Skyrmions and the Equation of State for Compact-Star Matter