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Punctual Presentability in Certain Classes of Algebraic Structures

Authors Dariusz Kalociński , Luca San Mauro , Michał Wrocławski

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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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