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Morphisms and BWT-Run Sensitivity

Authors Gabriele Fici , Giuseppe Romana , Marinella Sciortino , Cristian Urbina

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Formal languages and automata theory
  • Mathematics of computing → Combinatorics on words
Keywords
  • Burrows-Wheeler transform
  • BWT-runs
  • morphism
  • pure code
  • repetitiveness

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Abstract

We study how the application of morphisms affects the number r of equal-letter runs in the Burrows–Wheeler Transform (BWT). This parameter has emerged as a key repetitiveness measure in compressed indexing. We focus on the notion of BWT-run sensitivity after application of morphisms. For binary alphabets, we characterize the class of injective morphisms that preserve the number of BWT-runs up to a bounded additive increase by showing that it coincides with the known class of primitivity-preserving morphisms, which are those that map primitive words to primitive words. We further prove that deciding whether a given binary morphism has bounded BWT-run sensitivity is possible in polynomial time with respect to the total length of the images of the two letters. Additionally, we explore new structural and combinatorial properties of synchronizing and recognizable morphisms. These results establish new connections between BWT-based compressibility, code theory, and symbolic dynamics.

Cite As Get BibTex

Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. Morphisms and BWT-Run Sensitivity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.49

Author Details

Gabriele Fici
  • Department of Mathematics and Computer Science, University of Palermo, Italy
Giuseppe Romana
  • Department of Mathematics and Computer Science, University of Palermo, Italy
Marinella Sciortino
  • Department of Mathematics and Computer Science, University of Palermo, Italy
Cristian Urbina
  • Department of Computer Science, University of Chile, Santiago, Chile
  • Centre for Biotechnology and Bioengineering (CeBiB), Santiago, Chile

Funding

  • Fici, Gabriele: Supported by MUR project PRIN 2022 APML - 20229BCXNW, funded by the European Union – Mission 4 "Education and Research" C2 - Investment 1.1.
  • Romana, Giuseppe: Supported by the project "ACoMPA – Algorithmic and Combinatorial Methods for Pangenome Analysis" (CUP B73C24001050001) funded by the NextGeneration EU programme PNRR MUR M4 C2 Inv. 1.5 - Project ECS00000017 Tuscany Health Ecosystem (Spoke 6), CUP Master B63C22000680007 and by the INdAM - GNCS Project CUP_E53C24001950001.
  • Sciortino, Marinella: Supported by the MUR PRIN Project "PINC, Pangenome INformatiCs: from Theory to Applications" (Grant No. 2022YRB97K), funded by Next Generation EU PNRR M4 C2, Inv. 1.1 and by the INdAM - GNCS Project CUP_E53C24001950001.
  • Urbina, Cristian: Basal Funds FB0001 and AFB240001, ANID, Chile; FONDECYT Project 1-230755, ANID, Chile; ANID-Subdirección de Capital Humano/Doctorado Nacional/2021-21210580, ANID, Chile; NIC Chile Doctoral Scholarship, NIC, Chile.

References

  1. Tooru Akagi, Mitsuru Funakoshi, and Shunsuke Inenaga. Sensitivity of string compressors and repetitiveness measures. Information and Computation, 291:104999, 2023. URL: https://doi.org/10.1016/J.IC.2022.104999.
  2. Evelyne Barbin-Le Rest and Michel Le Rest. Sur la combinatoire des codes à deux mots. Theoretical Computer Science, 41:61-80, 1985. URL: https://doi.org/10.1016/0304-3975(85)90060-X.
  3. Marie-Pierre Béal, Dominique Perrin, and Antonio Restivo. Unambiguously coded shifts. European Journal of Combinatorics, 119:103812, 2024. URL: https://doi.org/10.1016/J.EJC.2023.103812.
  4. Jean Berstel, Dominique Perrin, and Christophe Reutenauer. Codes and Automata, volume 129 of Encyclopedia of mathematics and its applications. Cambridge University Press, 2010. Google Scholar
  5. Jean Berstel and Patrice Séébold. A Characterization of Sturmian Morphisms. In MFCS, volume 711 of Lecture Notes in Computer Science, pages 281-290. Springer, 1993. URL: https://doi.org/10.1007/3-540-57182-5_20.
  6. Michael Burrows and David Wheeler. A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation, 1994. Google Scholar
  7. Julien Cassaigne. An algorithm to test if a given circular HD0L-language avoids a pattern. In IFIP Congress (1), volume A-51 of IFIP Transactions, pages 459-464. North-Holland, 1994. Google Scholar
  8. Julien Cassaigne, France Gheeraert, Antonio Restivo, Giuseppe Romana, Marinella Sciortino, and Manon Stipulanti. New string attractor-based complexities for infinite words. Journal of Combinatorial Theory, Series A, 208:105936, 2024. URL: https://doi.org/10.1016/J.JCTA.2024.105936.
  9. Kuo Tsai Chen, Ralph H. Fox, and Roger C. Lyndon. Free differential calculus, IV. The quotient groups of the lower central series. Annals of Mathematics, 68(1):81-95, 1958. Google Scholar
  10. Wai-Fong Chuan. Sturmian morphisms and alpha-words. Theoretical Computer Science, 225(1-2):129-148, 1999. URL: https://doi.org/10.1016/S0304-3975(97)00239-9.
  11. Pál Dömösi, Sándor Horváth, Masami Ito, László Kászonyi, and Masashi Katsura. Formal languages consisting of primitive words. In Zoltán Ésik, editor, Fundamentals of Computation Theory, pages 194-203, Berlin, Heidelberg, 1993. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/3-540-57163-9_15.
  12. Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. On the Impact of Morphisms on BWT-Runs. In CPM, volume 259 of LIPIcs, pages 10:1-10:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.CPM.2023.10.
  13. Travis Gagie, Gonzalo Navarro, and Nicola Prezza. Fully Functional Suffix Trees and Optimal Text Searching in BWT-Runs Bounded Space. Journal of the ACM, 67(1):2:1-2:54, 2020. URL: https://doi.org/10.1145/3375890.
  14. Sara Giuliani, Shunsuke Inenaga, Zsuzsanna Lipták, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. Bit catastrophes for the Burrows-Wheeler transform. Theory of Computing Systems, 69(2):19, 2025. URL: https://doi.org/10.1007/S00224-024-10212-9.
  15. Štěpán Holub, Martin Raska, and Stepán Starosta. Binary codes that do not preserve primitivity. Journal of Automated Reasoning, 67(3):25, 2023. URL: https://doi.org/10.1007/S10817-023-09674-2.
  16. Cheng-Chi Huang. A note on pure codes. Acta Informatica, 47(5-6):347-357, 2010. URL: https://doi.org/10.1007/S00236-010-0122-7.
  17. Dominik Kempa and Nicola Prezza. At the roots of dictionary compression: string attractors. In STOC, pages 827-840. ACM, 2018. URL: https://doi.org/10.1145/3188745.3188814.
  18. Karel Klouda and Stepán Starosta. Characterization of circular D0L-systems. Theor. Comput. Sci., 790:131-137, 2019. URL: https://doi.org/10.1016/J.TCS.2019.04.021.
  19. Ben Langmead and Steven L. Salzberg. Fast gapped-read alignment with Bowtie 2. Nature Methods, 9(4):357-359, 2012. Google Scholar
  20. Ben Langmead, Cole Trapnell, Mihai Pop, and Steven L. Salzberg. Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biology, 10(3):R25, 2009. Google Scholar
  21. Heng Li and Richard Durbin. Fast and accurate long-read alignment with Burrows-Wheeler transform. Bioinformatics, 26(5):589-595, 2010. URL: https://doi.org/10.1093/BIOINFORMATICS/BTP698.
  22. M. Lothaire. Combinatorics on Words. Cambridge University Press, 1997. Google Scholar
  23. Roger C. Lyndon and Marcel-Paul Schützenberger. The equation a^m = bⁿ c^p in a free group. Michigan Mathematical Journal, 9(4):289-298, 1962. Google Scholar
  24. Sabrina Mantaci, Antonio Restivo, and Marinella Sciortino. Burrows-Wheeler transform and Sturmian words. Information Processing Letters, 86(5):241-246, 2003. URL: https://doi.org/10.1016/S0020-0190(02)00512-4.
  25. Victor Mitrana. Primitive morphisms. Information Processing Letters, 64(6):277-281, 1997. URL: https://doi.org/10.1016/S0020-0190(97)00178-6.
  26. Gonzalo Navarro. Indexing highly repetitive string collections, part I: Repetitiveness measures. ACM Computing Surveys, 54(2):article 29, 2021. Google Scholar
  27. Gonzalo Navarro. The compression power of the BWT: technical perspective. Communications of the ACM, 65(6):90, 2022. URL: https://doi.org/10.1145/3531443.
  28. Gonzalo Navarro and Cristian Urbina. Repetitiveness measures based on string morphisms. Theoretical Computer Science, 1043:115259, 2025. URL: https://doi.org/10.1016/J.TCS.2025.115259.
  29. Geneviève Paquin. On a generalization of Christoffel words: epichristoffel words. Theoretical Computer Science, 410(38-40):3782-3791, 2009. URL: https://doi.org/10.1016/J.TCS.2009.05.014.
  30. Antonio Restivo. On a Question of McNaughton and Papert. Information and Control, 25(1):93-101, 1974. URL: https://doi.org/10.1016/S0019-9958(74)90821-3.
  31. Michel Rigo. Formal Languages, Automata and Numeration Systems 1: Introduction to Combinatorics on Words. Wiley, 2014. Google Scholar
  32. Huei-Jan Shyr and Gabriel Thierrin. Codes, languages and MOL schemes. RAIRO Theoretical Informatics and Applications, 11(4):293-301, 1977. URL: https://doi.org/10.1051/ITA/1977110402931.
  33. Huei-Jan Shyr and Shyr-Shen Yu. Non-primitive words in the language p^+q^+. Soochow Journal of Mathematics, 20:535-546, 1994. Google Scholar
  34. Md. Vasimuddin, Sanchit Misra, Heng Li, and Srinivas Aluru. Efficient architecture-aware acceleration of BWA-MEM for multicore systems. In 2019 IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019, Rio de Janeiro, Brazil, May 20-24, 2019, pages 314-324, Los Alamitos, CA, 2019. IEEE Computer Society. URL: https://doi.org/10.1109/IPDPS.2019.00041.
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