I suppose that $\Sigma = \{a\}$.Prove or Disprove: For every polynomial $p(n)$ with coefficients in $\mathbb{N}$, $L = \{a^{p(n)} \; | \; n \in \mathbb{N}\}$ is a context sensitive language.It seems that it is a context sensitive language. I guess making LBA or context sensitive grammar is not easy for this language.  Can I prove this with closure property of CSL for example like complement?  Can any one help me to prove for instance $L_1 = \{a^{n^7+n^5+n^3+n^2+1} | n\in \mathbb{N}\}$ is context sensitive. Maybe I can get an idea from this to prove my first question.
Is unary language with polynomial power context sensitive?
formal languages;context sensitive