and a regular language is context-free, hence the variant of the problem where B is a regular grammar is decidable (see "Emptiness" below).
*Containment: is ? Again, the variant of the problem where B is a regular grammar is decidable, while that where A is regular is generally not.
*Universality: is ?
*Regularity: is a regular language?
*Ambiguity: is every grammar for ambiguous?

The following problems are decidable for arbitrary context-free languages:
*Emptiness: Given a context-free grammar A, is ?
*Finiteness: