characteristic vectors for systems
Yes.  You want to look at the bag-of-words model and n-gram models.

The bag-of-words model corresponds to the part of your characteristic vector: namely, the parts &lt;A&gt;, &lt;B&gt;, &lt;C&gt; of your characteristic vector, i.e., the frequencies of a single letter.  These are used as features for the ML algorithm.

n-gram models generalize this to a substring of length n.  For each substring of length n, we count the frequency of that substring.  These frequencies are again used as features.  For instance, we'd have a feature for the frequency of AB, the frequency of AC, and so on.

In real-world computer science, we don't deal with infinite systems; we only deal with finite systems.  (Our lifetime is finite, so a computer can only examine a finite portion of the input.)