today finish depth-3 homogeneous lbs polynomial identity testing depth-3 homogeneous recap lb for partial derive space of determinant PIT given polynomial is it zero PIT in RP Q. PIT in P? def: hitting set rmk: small explicit hitting sets => PIT \in P large explicit hitting sets exist, via schwartz-zippel small hitting sets exist, via prob-method hitting sets =~ lbs q. hitting sets for depth-3 hom? given small top-fan-in depth-3, you know it isn't the determinant def of sparse white-box vs black-box thm statement idea: hash to one variable use univariate interpolation