Employing internal quantum systems as reference frames is a crucial concept in gravity, gauge theories and foundations whenever external relata are unavailable. In this work, we give comprehensive self-contained treatment of such (QRFs) for the case when underlying configuration space finite Abelian group, significantly extending our previous work (Quantum 5, 530 (2021)). The simplicity setup a...

Some results from Dassow and Mitrana (Internat. J. Comput. Algebra (2000)), Griebach (Theoret. Comput. Sci. 7 (1978) 311) and Ibarra et al. (Theoret. Comput. Sci. 2 (1976) 271) are generalized for finite autómata over arbitrary groups. The closure properties of these autómata are poorer and the accepting power is smaller when abelian groups are considered. We prove that the addition of any abel...