A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits). Is it true ?
My attempt :
Arbitrary length means variable length, and there is no DFA to recognize arbitrary length number, since we need memory to store the number.
Does arbitrary number means (may be) number having infinite digits?
Somewhere, it's given FSM for "add two binary numbers of infinite length by the following FSM".
Can you please explain?
Arbitrary means arbitrary. That means that we put no restrictions on the number, but still each number is finite and has finite length.
This means that we a priori can't assume that it has less than, say $1234$ digits. All we can know is that if we start in one end it and step through we will eventually reach the other end.
Whether you can add them by a FSM depends on the requirement of input and outputs. If for example the numbers are fed into the FSM serially starting at LSD and the output is supposed to be fed out from the FSM serially starting at LSD you can certainly do it. It's the same algorithm you used when doing it by pen and paper - the only state you'll need is the carry.