Content-Type: text/shitpost

Subject: A formal language puzzle
Path: you!your-host!walldrug!central-scrutinizer!fpuzhpx!plovergw!ploverhub!shitpost!mjd
Date: 2021-03-14T14:09:10
Newsgroup: comp.lang.haskell.formal-language-question
Message-ID: <d72be256bce765f7@shitpost.plover.com>
Content-Type: text/shitpost

Suppose !!\mathcal L!! is a regular language and there is some string !!t!! that is a substring of every element of !!\mathcal L!!.

Is it necessarily the case that there must exist regular languages !!A!! and !!B!! such that $$\mathcal L = A t B?$$