of finitely many context-free languages. Poly-context-free groups include all finitely generated groups commensurable with groups embeddable in a direct product of finitely many free groups, and Brough conjectured that every poly-context-free group arises in this way. Ceccherini-Silberstein, Coornaert, Fiorenzi, Schupp, and Touikan introduced the notion of a multipass automaton, which are nondeterministic automata accepting precisely all the finite intersections of context-free languages. They also obtained results providing significant evidence in favor of the above conjecture of Brough. Nyberg-Brodda generalised the Muller-Schupp theorem from groups to ``special monoids", a class of semigroups containing, but strictly larger than, the class of groups, characterising such semigroups with a context-free word problem as being precisely those with a virtually free maximal subgroup. Subsequent to the 1983 paper of Muller and Schupp, several authors obtained alternate or simplified proofs of the Muller–Schupp theorem. See also Infinite tree automaton Word problem (mathematics) Formal language References External links Context-free groups and their structure trees, expository talk by Armin Weiß Geometric group theory Formal languages