Let $\mathcal{P} = ((\mathcal{A} ^i)_{i = 1}^{n}, (\mathcal{O} ^i)_{i = 1}^{n}, \preceq)$ be an $n$-stage decision problem with constant actions sets $\mathcal{A} ^t_{h} = U_t$ for each history $h \in H^{t-1}$. In other words, the actions available at stage $t$ do not depend on the history, only on the stage $t$.
A state representation
for $\mathcal{P} $ is tuple
\[
(\set{\mathcal{X} _t}_{t = 1}^{n+1}, \set{f_{t}: \mathcal{X} _t
\times \mathcal{U} _t \to \mathcal{X} _{t+1}}_{t = 1}^{n})
\]