English

Checking whether a word is Hamming-isometric in linear time

Data Structures and Algorithms 2022-08-09 v4 Formal Languages and Automata Theory

Abstract

A finite word ff is Hamming-isometric if for any two word uu and vv of same length avoiding ff, uu can be transformed into vv by changing one by one all the letters on which uu differs from vv, in such a way that all of the new words obtained in this process also avoid~ff. Words which are not Hamming-isometric have been characterized as words having a border with two mismatches. We derive from this characterization a linear-time algorithm to check whether a word is Hamming-isometric. It is based on pattern matching algorithms with kk mismatches. Lee-isometric words over a four-letter alphabet have been characterized as words having a border with two Lee-errors. We derive from this characterization a linear-time algorithm to check whether a word over an alphabet of size four is Lee-isometric.

Keywords

Cite

@article{arxiv.2106.10541,
  title  = {Checking whether a word is Hamming-isometric in linear time},
  author = {Marie-Pierre Béal and Maxime Crochemore},
  journal= {arXiv preprint arXiv:2106.10541},
  year   = {2022}
}
R2 v1 2026-06-24T03:23:24.506Z