MAF (pronounced to rhyme with Taff) stands for Monoid Automata Factory. MAF is an open source software package for computation of, and with, finite state automata. These automata usually represent the structure of a finitely presented group (or monoid), or a subgroup of such a group, the presentation being supplied as input by the user. When MAF’s computations succeed many questions about the input group, monoid or subgroup can be (and indeed already have been) answered by the files that have been output. A fuller description of these files, and the uses they may be put to, can be found in MAF: An overview. For now we remark only that they provide an effective, and often very fast, means of computing with a group’s elements. For example, on a modest PC, it is possible, in much less than one second, to draw a picture of the Cayley graph of an arbitrary hyperbolic triangle group, after first computing, and then using, automata able to enumerate group elements up to any desired word length. But MAF is capable of working with much more challenging groups than this. It has been able to settle, within a few hours, the finiteness question for several presentations, where other methods had not succeeded.

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