Morphisms on infinite alphabets, countable states automata and regular   sequences
  In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings. 
Jie-Meng Zhang, Jin Chen, Yingjun Guo and Zhixiong Wen
cs.FL