Quasi-Periodicity Under Mismatch Errors

Authors Amihood Amir, Avivit Levy, Ely Porat

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Author Details

Amihood Amir
  • Bar-Ilan University and Johns Hopkins University, Ramat-Gan, Israel
Avivit Levy
  • Shenkar College, Ramat-Gan, Israel
Ely Porat
  • Bar-Ilan University, Ramat-Gan, Israel

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Amihood Amir, Avivit Levy, and Ely Porat. Quasi-Periodicity Under Mismatch Errors. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Tracing regularities plays a key role in data analysis for various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. Part of the scientific process is understanding and explaining these regularities. A common notion to describe regularity in a string T is a cover or quasi-period, which is a string C for which every letter of T lies within some occurrence of C. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper we initiate the study of quasi-periodicity persistence under mismatch errors, and our goal is to characterize situations where a given quasi-periodic string remains quasi-periodic even after substitution errors have been introduced to the string. Our study results in proving necessary conditions as well as a theorem stating sufficient conditions for quasi-periodicity persistence. As an application, we are able to close the gap in understanding the complexity of Approximate Cover Problem (ACP) relaxations studied by [Amir 2017a, Amir 2017b] and solve an open question.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
  • Theory of computation → Pattern matching
  • Periodicity
  • Quasi-Periodicity
  • Cover
  • Approximate Cover


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