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 from $\mathcal{L}_1$ to $\mathcal{L}_2$ 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 a pushdown automaton 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 the following problems: (1)~deciding whether, for a given threshold $k$, the edit distance from a pushdown automaton to a finite automaton is at most $k$, and (2)~deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.

Source: arXiv.org:1504.08259

Volume: Volume 13, Issue 3

Published on: September 13, 2017

Accepted on: September 13, 2017

Submitted on: September 13, 2017

Keywords: Computer Science - Formal Languages and Automata Theory

Funding:

- Source : OpenAIRE Graph
*Modern Graph Algorithmic Techniques in Formal Verification*; Funder: Austrian Science Fund (FWF); Code: P 23499*Quantitative Reactive Modeling*; Funder: European Commission; Code: 267989*Formal methodes for the design and analysis of complex systems*; Funder: Austrian Science Fund (FWF); Code: Z 211*Quantitative Graph Games: Theory and Applications*; Funder: European Commission; Code: 279307

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