A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of cf languages: a generalization of the Chomsky-Schützenberger homomorphic characterization theorem, the Parikh theorem and a “pumping lemma” are proved. Multi-push-down languages are an AFL. Their recognizers are automata equipped with a multi-push-down tape. Multi-push-down languages form a hierarchy based on the number of push-down tapes.

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We introduce BD (Breadth-Depth) grammars which extend context-free grammars by allowing breadth-first derivations. Their languages are recognized by Deque (double ended queue) automata having a single state. BD languages also include languages recognized by monostatic queue automata. It is shown that the commutative image of BD languages is semilinear, that they have a periodicity (pumping) property, and can be homomorphically characterized as h(DAD∩R), where DAD is the Dyck-AntiDyck language, and R a regular set. Non-autoinclusive BD grammars coincide in power with breadth-first grammars with regular right parts.