Tower of algorithms
= Tower of algorithms
A tower of algorithms of height $k$ is a family $\Gamma_{n_k,\ldots,n_1}$ of finite-information algorithms such that
$$
\Xi(A)=\lim_{n_k\to\infty}\cdots\lim_{n_1\to\infty}\Gamma_{n_k,\ldots,n_1}(A)
$$
for every input $A$. The <Solvability complexity index> is the least possible height.