Beyond Generalized Multiplicities: Register Machines over Groups

Register machines are a classic model of computing, often seen as a canonical example of a device manipulating natural numbers. In this paper, we de ne register machines operating on general groups instead. This generalization follows the research direction started in multiple previous works. We study the expressive power of register machines as a function of the underlying groups, as well as of allowed ingredients (zero test, partial blindness, forbidden regions). We put forward a fundamental connection between register machines and vector addition systems. Finally, we show how registers over free groups can be used to store and manipulate strings.