Modulated String Searching
Alberto Apostolico, P\'eter L. Erd\H{o}s, Istv\'an Mikl\'os, Johannes, Siemons

TL;DR
This paper introduces modulated string searching, a unified framework combining numerical and Boolean conditions for string matching, enabling solutions for problems like locally bounded L1-norm matching that were previously unsolvable.
Contribution
It proposes a new generalized framework for string matching that integrates numerical and decision conditions, addressing problems lacking prior efficient solutions.
Findings
Defines modulated string searching as a unifying framework.
Addresses locally bounded L1-norm matching problem.
Provides potential for new efficient algorithms.
Abstract
In his 1987 paper entitled "Generalized String Matching", Abrahamson introduced {\em pattern matching with character classes} and provided the first efficient algorithm to solve it. The best known solution to date is due to Linhart and Shamir (2009). Another broad yet comparatively less studied class of string matching problems is that of numerical string searching, such as, e.g., the `less-than' or -norm string searching. The best known solutions for problems in this class are based on FFT convolution after some suitable re-encoding. The present paper introduces {\em modulated string searching} as a unified framework for string matching problems where the numerical conditions can be combined with some Boolean/numerical decision conditions on the character classes. One example problem in this class is the {\em locally bounded -norm} matching problem on character classes:…
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