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.

We show that the word problem is decidable for an amalgamated free product of finite inverse\ud semigroups (in the category of inverse semigroups). This is in contrast to a recent result of M. Sapir\ud that shows that the word problem for amalgamated free products of finite semigroups (in the category\ud of semigroups) is in general undecidable

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