The edit distance between two words $w_1, w_2$ is the minimal number of wordoperations (letter insertions, deletions, and substitutions) necessary totransform $w_1$ 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 atmost $k$. We study the edit distance computation problem between pushdownautomata and their subclasses. The problem of computing edit distance to apushdown automaton is undecidable, and in practice, the interesting question isto compute the edit distance from a pushdown automaton (the implementation, astandard model for programs with recursion) to a regular language (thespecification). In this work, we present a complete picture of decidability andcomplexity for the following problems: (1)~deciding whether, for a giventhreshold $k$, the edit distance from a pushdown automaton to a finiteautomaton is at most $k$, and (2)~deciding whether the edit distance from apushdown automaton to a finite automaton is finite.
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机译:两个单词$ w_1,w_2 $之间的编辑距离是将$ w_1 $转换为$ w_2 $所需的最小字操作次数(字母插入,删除和替换)。编辑距离可概括为以下语言:$ mathcal {L} _1, mathcal {L} _2 $,其中$ mathcal {L} _1 $到$ mathcal {L} _2 $的编辑距离是最小数$ k $,这样对于$ mathcal {L} _1 $中的每个单词,在$ mathcal {L} _2 $中都存在一个单词,其编辑距离最大为$ k $。我们研究了下推自动机及其子类之间的编辑距离计算问题。计算到达下推式自动机的编辑距离的问题尚不确定,并且在实践中,有趣的问题是计算从下推式自动机(实现,具有递归的程序的标准模型)到常规语言(规范)的编辑距离。在这项工作中,我们给出了以下问题的可判定性和复杂性的完整描述:(1)〜确定对于给定阈值$ k $,下推自动机到有限自动机的编辑距离是否最多为$ k $,并且( 2)〜确定从下推自动机到有限自动机的编辑距离是否是有限的。
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