The Relative Edit-Distance Between Two Input-Driven Languages

Hyunjoon Cheon, Yo-Sub Han, Sang-Ki Ko, Kai Salomaa

Abstract: We study the relative edit-distance problem between two input-driven languages. The relative edit-distance is closely related to the language inclusion problem, which is a crucial problem in formal verification. Input-driven languages are a robust subclass of context-free languages that enable to model program analysis questions within tractable time complexity. For instance, the language inclusion (or equivalence) problem is undecidable for context-free languages whereas the problem is solvable in polynomial time for input-driven languages specified by deterministic input-driven pushdown automata (IDPDAs) and is EXPTIME-complete for nondeterministic IDPDAs. Our main contribution is to prove that the relative edit-distance problem for two input-driven languages is decidable by designing a polynomial time IDPDA construction, based on the edit-distance, that recognizes a neighbourhood of a given input-driven language. In fact, the relative edit-distance problem between two input-driven languages turns out to be EXPTIME-complete when the neighbourhood distance threshold is fixed as a constant.