Edit Distance for Pushdown Automata

Krishnendu Chatterjee, Thomas A. Henzinger, Rasmus Ibsen-Jensen, Jan Otop

Abstract: The edit distance between two words \(w_1, w_2\) is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform \(w_1\) to \(w_2\). The edit distance generalizes to languages \(\mathcal {L}_1, \mathcal {L}_2\), where the edit distance is the minimal number k such that for every word from \(\mathcal {L}_1\) there exists a word in \(\mathcal {L}_2\) with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.