On the Equivalence Problem for E-Pattern Languages

On the one hand, the inclusion problem for nonerasing and erasing pattern languages is undecidable (see JSSY93]). On the other hand, the language equivalence problem for nonerasing pattern languages is trivially decidable (see Ang80a]) but the question of whether the same holds for erasing pattern languages is still open. It has been conjectured by Jiang et al. JSSY93] that the language equivalence problem for erasing pattern languages is also decidable. In this paper, we introduce a new normal form for patterns and show, using the normal form, that the language equivalence problem for erasing pattern languages is decidable in many special cases. We conjecture that our normal form procedure decides the problem in the general case, too. If the conjecture holds true, then the normal form is the shortest pattern generating a given erasing pattern language.