On the equivalence problem for E-pattern languages (extended abstract)

Abstract

On the one hand, the inclusion problem for nonerasing and erasing pattern languages is undecidable; see [JSSY95]. On the other hand, the language equivalence problem for NE-pattern languages is trivially decidable (see [AngS0a]) but the question of whether the same holds for E-pattern languages is still open. It has been conjectured by Jiang et al. [JSSY95] that the language equivalence problem for E-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 E-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 E-pattern language.