Decidable and Undecidable Fragments of First-Order Concatenation Theory

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results. This is a post-peer-review, pre-copyedit version of an article. The final authenticated version is available online at: https://link.springer.com