Can undead and constructs regain hit points after a short/long rest?

Any creature, including undead and constructs, can use its HD during a short rest to regain hit points. #DnD

— Jeremy Crawford (@JeremyECrawford) January 12, 2017

Any creature, including undead and constructs, can take a long rest to regain all its hit points. #DnD

— Jeremy Crawford (@JeremyECrawford) January 12, 2017

@Zardozindustry I take it this has come up a lot since Monday? It's come up before, particularly in relation to a necromancer's undead minions.

— Jeremy Crawford (@JeremyECrawford) January 12, 2017