Undecidability of the word problem for Yamamura’s HNN-extension under nice conditions

Abstract

The solvability of the word problem for Yamamura’s HNN-extensions [S; A1, A2; ϕ] has been proved in some particular cases. However, we show that, contrary to the group case, the word problem for [S; A1A2; ϕ] is undecidable even if we consider S to have finite R-classes, A1 and A2 to be free inverse subsemigroups of finite rank and with zero, and ϕ , ϕ−1 to be computable.