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Punctual Presentability in Certain Classes of Algebraic Structures

Authors Dariusz Kalociński , Luca San Mauro , Michał Wrocławski

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computability
Keywords
  • fully primitive recursive structures
  • punctual presentability
  • trees
  • injection structures

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Abstract

Punctual structure theory is a rapidly emerging subfield of computable structure theory which aims at understanding the primitive recursive content of algebraic structures. A structure with domain ℕ is punctual if its relations and functions are (uniformly) primitive recursive. One of the fundamental problems of this area is to understand which computable members of a given class of structures admit a punctual presentation. We investigate such a problem for a number of familiar classes of algebraic structures, paying special attention to the case of trees, presented both in a relational and functional signature.

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Dariusz Kalociński, Luca San Mauro, and Michał Wrocławski. Punctual Presentability in Certain Classes of Algebraic Structures. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 65:1-65:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.65

Author Details

Dariusz Kalociński
  • Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland
Luca San Mauro
  • Department of Philosophy, University of Bari, Italy
Michał Wrocławski
  • Faculty of Philosophy, University of Warsaw, Poland

Funding

  • Kalociński, Dariusz: supported by the National Science Centre Poland grant under the agreement no. 2023/49/B/HS1/03930.
  • San Mauro, Luca: is a member of INDAM-GNSAGA.
  • Wrocławski, Michał: supported by the National Science Centre Poland grant under the agreement no. 2023/49/B/HS1/03930.

Acknowledgements

We would like to thank the reviewers as well as Nikolay Bazhenov, Ivan Georgiev and Stefan Vatev for helpful discussions.

References

  1. Pavel E. Alaev and Viktor L. Selivanov. Polynomial computability of fields of algebraic numbers. Doklady Mathematics, 98(1):341-343, 2018. URL: https://doi.org/10.1134/S1064562418050137.
  2. Nikolay Bazhenov, Rod Downey, Iskander Kalimullin, and Alexander Melnikov. Foundations of online structure theory. Bulletin of Symbolic Logic, 25(2):141-181, 2019. Publisher: Cambridge University Press. URL: https://doi.org/10.1017/bsl.2019.20.
  3. Nikolay Bazhenov, Iskander Kalimullin, Alexander Melnikov, and Keng Meng Ng. Online presentations of finitely generated structures. Theoretical Computer Science, 844:195-216, 2020. URL: https://doi.org/10.1016/j.tcs.2020.08.021.
  4. Nikolay Bazhenov, Keng Meng Ng, Luca San Mauro, and Andrea Sorbi. Primitive recursive equivalence relations and their primitive recursive complexity. Computability, 11(3-4):187-221, 2022. URL: https://doi.org/10.3233/COM-210375.
  5. Nilkolay Bazhenov, Matthew Harrison-Trainor, Iskander Kalimullin, Alexander Melnikov, and Keng Meng Ng. Automatic and polynomial-time algebraic structures. The Journal of Symbolic Logic, 84(4):1630-1669, 2019. URL: https://doi.org/10.1017/jsl.2019.26.
  6. Douglas Cenzer, Valentina Harizanov, and Jeffrey B. Remmel. Computability-theoretic properties of injection structures. Algebra and Logic, 53(1):39-69, 2014. URL: https://doi.org/10.1007/s10469-014-9270-0.
  7. Douglas Cenzer and Jeffrey B. Remmel. Polynomial-time versus recursive models. Annals of Pure and Applied Logic, 54(1):17-58, 1991. URL: https://doi.org/10.1016/0168-0072(91)90008-A.
  8. Douglas Cenzer and Jeffrey B. Remmel. Polynomial-time abelian groups. Annals of Pure and Applied Logic, 56(1):313-363, 1992. URL: https://doi.org/10.1016/0168-0072(92)90076-C.
  9. Douglas Cenzer and Jeffrey B. Remmel. Feasible graphs with standard universe. Annals of Pure and Applied Logic, 94(1):21-35, 1998. URL: https://doi.org/10.1016/S0168-0072(97)00064-X.
  10. Rod Downey, Noam Greenberg, Alexander Melnikov, Keng Meng Ng, and Daniel Turetsky. Punctual categoricity and universality. The Journal of Symbolic Logic, 85(4):1427-1466, 2020. URL: https://doi.org/10.1017/jsl.2020.51.
  11. Noam Greenberg, Matthew Harrison-Trainor, Alexander Melnikov, and Dan Turetsky. Non-density in punctual computability. Annals of Pure and Applied Logic, 172(9):102985, 2021. URL: https://doi.org/10.1016/j.apal.2021.102985.
  12. Iskander Kalimullin, Alexander Melnikov, and Keng Meng Ng. Algebraic structures computable without delay. Theoretical Computer Science, 674:73-98, 2017. URL: https://doi.org/10.1016/j.tcs.2017.01.029.
  13. Bakhadyr Khoussainov and Anil Nerode. Automatic presentations of structures. In Daniel Leivant, editor, Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 367-392. Springer Berlin Heidelberg, 1995. URL: https://doi.org/10.1007/3-540-60178-3_93.
  14. Anatolii I. Mal'tsev. Constructive algebras i. Russian Mathematical Surveys, 16(3):77, 1961. URL: https://doi.org/10.1070/RM1961v016n03ABEH001120.
  15. Antonio Montalbán. Computable structure theory: Within the arithmetic. Cambridge University Press, 2021. Google Scholar
  16. Michael O. Rabin. Computable algebra, general theory and theory of computable fields. Transactions of the American Mathematical Society, 95(2):341-360, 1960. URL: https://doi.org/10.2307/1993295.
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