Decidability Versus Undecidability of the Word Problem in Amalgams of Inverse Semigroups

Abstract

This paper is a survey of some recent results on the word problem for amalgams of inverse semigroups. Some decidability results for special types of amalgams are summarized pointing out where and how the conditions posed on amalgams are used to guarantee the decidability of the word problem. Then a recent result on undecidability is shortly illustrated to show how small is the room between decidability and undecidability of the word problem in amalgams of inverse semigroups.