On the Complexity of Automatic Complexity

Generalizing the notion of automatic complexity of individual words due to Shallit and Wang, we define the automatic complexity A(E) of an equivalence relation E on a finite set S of words. We prove that the problem of determining whether A(E) equals the number |E| of equivalence classes of E is NP-complete. The problem of determining whether A(E) = |E| + k… CONTINUE READING