If we use the notation where when we say:
$$M = M(G)$$
We mean to say that $M$ is a automata with states and alphabet elements of $G$.
From here, I am posed this question (Abstract Algebra by Pinter):
Describe $M(Z_4)$, give the table of its next-state function as well as its state diagram.
I cannot understand how I am to do this, since
- I'm not given an operation (although I suspect it is assumed to be multiplication)
- If I do multiplication over $Z_4$, it gives me a infinite state diagram, which I do not quite understand.