‘Cancellativity is undecidable for automatic semigroups’
Quarterly Journal of Mathematics, 57, no. 3 (2006), pp. 285–295.
DOI: 10.1093/qmath/hai023. MR: 2253587. ZBL: 1126.20039.

Abstract

Via an encoding of the Modified Post’s Correspondence Problem, this paper shows that it is undecidable whether an automatic semigroup is cancellative.