This paper reviews the recent progress in the research of equation of state of dense matter for supernova simulations, The equation of state plays an important role to clarify the mechanism of core-collapse supernovae, the formation of compact objects and the properties of supernova neutrinos. We describe the problems of explosion mechanism in current supernova simulations, putting emphasis on the equation of state. We discuss also the topics on the birth of neutron stars (or black holes) and the associated neutrino bursts, which reflect the properties of dense matter.
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