On the equivalence problem for E-pattern languages over small alphabets

We contribute new facets to the discussion on the equivalence problem for E-pattern languages (also referred to as extended or erasing pattern languages). This fundamental open question asks for the existence of a computable function that, given any pair of patterns, decides whether or not they generate the same language. Our main result disproves Ohlebusch and Ukkonen’s conjecture (Theoretical Computer Science 186, 1997) on the equivalence problem; the respective argumentation, that largely deals with the nondeterminism of pattern languages, is restricted to terminal alphabets with at most four distinct letters.