  $\operatorname{Holant}^*(f)$ denotes a class of counting problems specified
by a constraint function $f$. We prove complexity dichotomy theorems for
$\operatorname{Holant}^*(f)$ in two settings: (1) $f$ is any arity-3
real-valued function on input of domain size 3. (2) $f$ is any arity-3
$\{0,1\}$-valued function on input of domain size 4.
