How to handle dfa with countless states? I have a question regarding DFA:

Design a DFA M with alphabet $\sum = \ {\{0,1,2,R}\}$ where the states remember actual sums of the number, except that the sum is reset to 0 whenever the symbol $R$ appears. Show diagrammatically how this DFA can be constructed. What is the problem with this DFA?

One thing I do understand is that in order to remember the actual sums I would have to have the sums as states. But sums can be any number from 0 to  infinity. So would the states increase exponentially while reading the input string? How can I tackle this problem?
You seem to have missed the last sentence of the question:


  What is the problem with this DFA?


The problem with this DFA is that it isn't finite (so it's not really a DFA).

A DFA is a static object &mdash; the only way it interacts with the environment is by switching states.