  Let $D_n$ denote the set of monotone Boolean functions with $n$ variables.
Elements of $D_n$ can be represented as strings of bits of length $2^n$. Two
elements of $D_0$ are represented as 0 and 1 and any element $g\in D_n$, with
$n>0$, is represented as a concatenation $g_0\cdot g_1$, where $g_0, g_1\in
D_{n-1}$ and $g_0\le g_1$. For each $x\in D_n$, we have dual $x^*\in D_n $
which is obtained by reversing and negating all bits. An element $x\in D_n$ is
self-dual if $x=x^*$. Let $\lambda_n$ denote the cardinality of the set of all
self-dual monotone Boolean functions of $n$ variables. The value $\lambda_n$ is
also known as the $n$-th Hosten-Morris number. In this paper, we derive several
algorithms for counting self-dual monotone Boolean functions and confirm the
known result that $\lambda_9$ equals 423,295,099,074,735,261,880.
