Minsky machines and algorithmic problems

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.Comment: 19 page

On the Tits alternative for PD(3)PD(3) groups

We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group.Comment: 16 pages, minor corrections, to appear in Ann. Fac. Sci. Toulouse Mat