# A language outside the Boolean closure of stochastic languages

Stochastic languages, that is, those accepted by probabilistic automata, are known to not be closed under intersection, union, concatenation, and morphism, even on unary languages.

I have two questions about the Boolean closure of the class of stochastic languages:

1. Is this class closed under morphisms or concatenation?
2. Can we show that $\{a^{2^n} \mid n \in \mathbb{N}\}$ is not in it?

Many thanks!

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