$L$ is defined over the alphabet $\{a,b\}$ and it's decidable.The language is $\mathrm{perm}(L)$ which is the set of all permutations of all words in $L$.So far my proof is the following:Construct a TM $M$ that decides the language $\mathrm{perm}(L)$. $M$ has input $w$.Let $\pi(w)$ be a random permutation of w. Then feed it to $M$: $M$ accepts if $\pi(w) \in L$ or rejects if $\pi(w) \notin L$. I.e. if we let $\pi(w)$ be a permutation of $w$ s.t. $\pi(w) \in L$, $M$ should halt and accept.If we let $\pi(w)$ be a permutation of $w$ s.t. $\pi(w) \notin L$, $M$ should halt and reject.Is this correct and enough?
Prove this language is decidable?
computability;permutations