Tootfinder

Edit Distance of Finite State Transducers
C. Aiswarya, Amaldev Manuel, Saina Sunny
https://arxiv.org/abs/2404.16518 https://arxiv.org/pdf/2404.16518
arXiv:2404.16518v1 Announce Type: new
Abstract: We lift metrics over words to metrics over word-to-word transductions, by defining the distance between two transductions as the supremum of the distances of their respective outputs over all inputs. This allows to compare transducers beyond equivalence.
Two transducers are close (resp. $k$-close) with respect to a metric if their distance is finite (resp. at most $k$). Over integer-valued metrics computing the distance between transducers is equivalent to deciding the closeness and $k$-closeness problems. For common integer-valued edit distances such as, Hamming, transposition, conjugacy and Levenshtein family of distances, we show that the closeness and the $k$-closeness problems are decidable for functional transducers. Hence, the distance with respect to these metrics is also computable.
Finally, we relate the notion of distance between functions to the notions of diameter of a relation and index of a relation in another. We show that computing edit distance between functional transducers is equivalent to computing diameter of a rational relation and both are a specific instance of the index problem of rational relations.

This https://arxiv.org/abs/2204.02201 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the size distribution of Levenshtein balls with radius one
The fixed length Levenshtein (FLL) distance between two words $\mathbf{x,y} \in \mathbb{Z}_m^n$ is the smallest integer $t$ such that $\mathbf{x}$ can be transformed to $\mathbf{y}$ by $t$ insertions and $t$ deletions. The size of a ball in FLL metric is a fundamental but challenging problem. Very recently, Bar-Lev, Etzion, and Yaakobi explicitly determined the minimum, maximum and average sizes of the FLL balls with radius one. In this paper, based on these results, we further prove that the s…

Leveraging Large Language Models for Fuzzy String Matching in Political Science
Yu Wang
https://arxiv.org/abs/2403.18218 https://arxi…

Leveraging Large Language Models for Fuzzy String Matching in Political Science
Fuzzy string matching remains a key issue when political scientists combine data from different sources. Existing matching methods invariably rely on string distances, such as Levenshtein distance and cosine similarity. As such, they are inherently incapable of matching strings that refer to the same entity with different names such as ''JP Morgan'' and ''Chase Bank'', ''DPRK'' and ''North Korea'', ''Chuck Fleischmann (R)'' and ''Charles Fleischmann (R)''. In this letter, we propose to use larg…