# complexity theory – Can you say anything interesting about a language knowing only that it is prefix-closed?

Suppose $$L$$ is an arbitrary formal language over a finite alphabet $$A$$, and suppose that $$L$$ is closed under prefixes (i.e. if $$w in L$$, and $$u$$ is any prefix of $$w$$, then $$u in L$$).

Knowing only this, can you give any positive or negative decidability or complexity results about $$L$$?

Thanks! 🙂