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We introduce the notion of multipass automata as a generalization of pushdownautomata and study the classes of languages accepted by such machines. Theclass of languages accepted by deterministic multipass automata is exactly theBoolean closure of the class of deterministic context-free languages while theclass of languages accepted by nondeterministic multipass automata is exactlythe class of poly-context-free languages, that is, languages which are theintersection of finitely many context-free languages. We illustrate the use ofthese automata by studying groups whose word problems are in the above classes.

Multipass automata and group word problems