On the decidability of the word problem for amalgamated free products of inverse semigroups

Hnn - Extensions of F Inite I Nverse S Emigroups

THE concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic problems. In inverse semigroup theory there are many ways of constructing HNNextension in order to ensure the embeddability of the original inverse semigroup in the new one...

Decidability and Tameness in the Theory of Finite Semigroups

Semigroups with inverse skeletons and Zappa-Sz$acute{rm e}$p products

The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ Esubseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${mathc...

Amalgams of inverse semigroups and reversible two-counter machines

We show that the word problem for an amalgam [S1, S2;U,ω1, ω2] of inverse semigroups may be undecidable even if we assume S1 and S2 (and therefore U) to have finite R-classes and ω1, ω2 to be computable functions, interrupting a series of positive decidability results on the subject. This is achieved by encoding into an appropriate amalgam of inverse semigroups 2-counter machines with sufficien...

N ov 2 00 8 Compressed word problems in HNN - extensions and amalgamated products

It is shown that the compressed word problem for an HNNextension 〈H, t | tat = φ(a)(a ∈ A)〉 with A finite is polynomial time Turing-reducible to the compressed word problem for the base group H . An analogous result for amalgamated free products is shown as well.