Inverse semigroups with rational word problem are finite

Deciding Word Problems of Semigroups using Finite State Automata

We explore natural classes of finitely generated semigroups that have word problem decidable by synchronous or asynchronous two-tape finite state automata. Synchronous two-tape automata decide regular word problems and asynchronous automata decide rational word problems. We argue that asynchronous two-tape automata are a more suitable choice than synchronous two-tape automata and show that the ...

On the Complexity of the Word Problem of Automaton Semigroups and Automaton Groups

In this paper, we study the word problem of automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace...

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...

The Uniform Word Problem for Groups and Finite Rees Quotients of E-unitary Inverse Semigroups

Decidability and Tameness in the Theory of Finite Semigroups