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Transducers on Compressed Strings

Authors Mikołaj Bojańczyk , Markus Lohrey

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LIPIcs.ICALP.2026.170.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
Keywords
  • polyregular functions
  • grammar compression

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Abstract

We study string-to-string functions which are compatible with compression in the following sense: given a compressed representation of an input string, one can compute in polynomial time a compressed representation of the output string. As the compression formalism, we use straight-line programs (i.e. context-free grammars that produce only one string). As the functions, we use finite state transducers, with a focus on the regular and polyregular functions. We show that all regular functions are compatible with compression, but this is no longer true for the polyregular functions. We identify a subclass of the polyregular functions - the so-called rectangular polyregular functions - which is compatible with compression, and we characterise this subclass in terms of a functional programming language.

Cite As Get BibTex

Mikołaj Bojańczyk and Markus Lohrey. Transducers on Compressed Strings. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 170:1-170:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.170

Author Details

Mikołaj Bojańczyk
  • University of Warsaw, Poland
Markus Lohrey
  • University of Siegen, Germany

Funding

  • Bojańczyk, Mikołaj: Mikołaj Bojańczyk was supported by the Polish National Science Centre (NCN) grant "Polynomial finite state computation" (2022/46/A/ST6/00072).

References

  1. Rajeev Alur and Pavol Cerný. Expressiveness of streaming string transducers. In Kamal Lodaya and Meena Mahajan, editors, Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, volume 8 of LIPIcs, pages 1-12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2010.1.
  2. Frédérique Bassino, Ilya Kapovich, Markus Lohrey, Alexei Miasnikov, Cyril Nicaud, Andrey Nikolaev, Igor Rivin, Vladimir Shpilrain, Alexander Ushakov, and Pascal Weil. Compression techniques in group theory. In Complexity and Randomness in Group Theory, chapter 4. De Gruyter, 2020. URL: https://doi.org/10.1515/9783110667028-004.
  3. Jean Berstel. Transductions and context-free languages. Springer-Verlag, 2013. URL: https://doi.org/10.1007/978-3-663-09367-1.
  4. Jean Berstel and Srecko Brlek. On the length of word chains. Information Processing Letters, 26(1):23-28, 1987. URL: https://doi.org/10.1016/0020-0190(87)90031-7.
  5. Alberto Bertoni, Christian Choffrut, and Roberto Radicioni. Literal shuffle of compressed words. In Proceedings of the Fifth IFIP International Conference On Theoretical Computer Science - TCS 2008, IFIP 20th World Computer Congress, TC 1, Foundations of Computer Science, volume 273 of IFIP, pages 87-100. Springer, 2008. URL: https://doi.org/10.1007/978-0-387-09680-3_6.
  6. Mikołaj Bojańczyk. Polyregular functions, 2018. URL: https://arxiv.org/abs/1810.08760.
  7. Mikołaj Bojańczyk. Transducers of polynomial growth. In Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '22. ACM, 2022. URL: https://doi.org/10.1145/3531130.3533326.
  8. Mikołaj Bojańczyk. Folding interpretations. In Proceedings of the 38th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2023, pages 1-13. IEEE, 2023. URL: https://doi.org/10.1109/LICS56636.2023.10175796.
  9. Mikołaj Bojańczyk, Laure Daviaud, and Shankara Narayanan Krishna. Regular and First-Order List Functions. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, pages 125-134. ACM, 2018. URL: https://doi.org/10.1145/3209108.3209163.
  10. Mikolaj Bojanczyk, Sandra Kiefer, and Nathan Lhote. String-to-string interpretations with polynomial-size output. In Proceedings of the 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, volume 132 of LIPIcs, pages 106:1-106:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.106.
  11. Mikołaj Bojańczyk and Rafał Stefański. Single-use automata and transducers for infinite alphabets. In Proceedings of the 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, volume 168 of LIPIcs, pages 113:1-113:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.113.
  12. Moses Charikar, Eric Lehman, Ding Liu, Rina Panigrahy, Manoj Prabhakaran, Amit Sahai, and Abhi Shelat. The smallest grammar problem. IEEE Transactions on Information Theory, 51(7):2554-2576, 2005. URL: https://doi.org/10.1109/TIT.2005.850116.
  13. Francisco Claude, Gonzalo Navarro, and Alejandro Pacheco. Grammar-compressed indexes with logarithmic search time. Journal of Computer and System Sciences, 118:53-74, 2021. URL: https://doi.org/10.1016/j.jcss.2020.12.001.
  14. Samuel Eilenberg. Automata, Languages, and Machines. Vol. A. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York, 1974. Google Scholar
  15. Joost Engelfriet and Hendrik Jan Hoogeboom. MSO definable string transductions and two-way finite-state transducers. ACM Transactions on Computational Logic, 2(2):216-254, 2001. URL: https://doi.org/10.1145/371316.371512.
  16. Joost Engelfriet and Heiko Vogler. Macro tree transducers. Journal of Computer and System Sciences, 31(1):71-146, 1985. URL: https://doi.org/10.1016/0022-0000(85)90066-2.
  17. Paolo Ferragina and Giovanni Manzini. Indexing compressed text. Journal of the ACM, 52(4):552-581, 2005. URL: https://doi.org/10.1145/1082036.1082039.
  18. Emmanuel Filiot and Pierre-Alain Reynier. Copyful streaming string transducers. In Proceedings of the 11th International Workshop on Reachability Problems, RP 2017, volume 10506 of Lecture Notes in Computer Science, pages 75-86. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-67089-8_6.
  19. Yoram Hirshfeld, Mark Jerrum, and Faron Moller. A polynomial-time algorithm for deciding equivalence of normed context-free processes. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, FOCS 1994, pages 623-631. IEEE Computer Society, 1994. URL: https://doi.org/10.1109/SFCS.1994.365729.
  20. Artur Jeż. Approximation of grammar-based compression via recompression. Theoretical Computer Science, 592:115-134, 2015. URL: https://doi.org/10.1016/J.TCS.2015.05.027.
  21. Artur Jeż. Faster fully compressed pattern matching by recompression. ACM Transactions on Algorithms, 11(3):20:1-20:43, 2015. URL: https://doi.org/10.1145/2631920.
  22. Marek Karpinski, Wojciech Rytter, and Ayumi Shinohara. Pattern-matching for strings with short descriptions. In Proceedings of the 6th Annual Symposium on Combinatorial Pattern Matching, CPM 95, volume 937 of Lecture Notes in Computer Science, pages 205-214. Springer, 1995. URL: https://doi.org/10.1007/3-540-60044-2_44.
  23. Sandra Kiefer, Lê Thành Dũng Nguyên, and Cécilia Pradic. Refutations of pebble minimization via output languages, 2023. URL: https://arxiv.org/abs/2301.09234.
  24. Yury Lifshits, Shay Mozes, Oren Weimann, and Michal Ziv-Ukelson. Speeding up HMM decoding and training by exploiting sequence repetitions. Algorithmica, 54(3):379-399, 2009. URL: https://doi.org/10.1007/S00453-007-9128-0.
  25. Markus Lohrey. Leaf languages and string compression. Information and Computation, 209(6):951-965, 2011. URL: https://doi.org/10.1016/J.IC.2011.01.009.
  26. Markus Lohrey. Algorithmics on SLP-compressed strings: A survey. Groups Complexity Cryptology, 4(2):241-299, 2012. URL: https://doi.org/10.1515/GCC-2012-0016.
  27. Markus Lohrey. The Compressed Word Problem for Groups. SpringerBriefs in Mathematics. Springer, 2014. URL: https://doi.org/10.1007/978-1-4939-0748-9.
  28. Kurt Mehlhorn, R. Sundar, and Christian Uhrig. Maintaining dynamic sequences under equality-tests in polylogarithmic time. In Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1994, pages 213-222. ACM/SIAM, 1994. URL: http://dl.acm.org/citation.cfm?id=314464.314496.
  29. Lê Thành Dung Nguyên, Camille Noûs, and Pierre Pradic. Comparison-free polyregular functions. In Proceedings of the 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, volume 198 of LIPIcs, pages 139:1-139:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.139.
  30. Wojciech Plandowski. Testing equivalence of morphisms on context-free languages. In Proceedings of the 2nd Annual European Symposium on Algorithms, ESA 1994, volume 855 of Lecture Notes in Computer Science, pages 460-470. Springer, 1994. URL: https://doi.org/10.1007/BFB0049431.
  31. Wojciech Plandowski and Wojciech Rytter. Complexity of language recognition problems for compressed words. In Juhani Karhumäki, Hermann A. Maurer, Gheorghe Paun, and Grzegorz Rozenberg, editors, Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa, pages 262-272. Springer, 1999. URL: https://doi.org/10.1007/978-3-642-60207-8_23.
  32. Wojciech Rytter. Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theoretical Computer Science, 302(1-3):211-222, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00777-6.
  33. John C. Shepherdson. The reduction of two-way automata to one-way automata. IBM Journal of Research and Development, 3(2):198-200, April 1959. URL: https://doi.org/10.1147/RD.32.0198.
  34. Morten Heine Sørensen and Pawel Urzyczyn. Lectures on the Curry-Howard Isomorphism. Elsevier, 2006. URL: https://www.sciencedirect.com/bookseries/studies-in-logic- and-the-foundations-of-mathematics/vol/149.
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