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A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations

Authors Melissa Antonelli , Arnaud Durand , Juha Kontinen

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Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Circuit complexity
Keywords
  • Implicit computational complexity
  • parallel computation
  • ordinary differential equations
  • circuit complexity

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Abstract

Implicit computational complexity is an active area of theoretical computer science, which aims at providing machine-independent characterizations of relevant complexity classes. One of the seminal works in this field appeared in 1965, when Cobham introduced a function algebra closed under bounded recursion on notation to capture FP. Later on, several complexity classes have been characterized using limited recursion schemas. In this context, a new approach was recently introduced, showing that ordinary differential equations (ODEs) offer a natural tool for algorithmic design and providing a characterization of FP by an ODE-schema. The overall goal of the present work is precisely that of generalizing this approach to parallel computation, obtaining an original ODE-characterization for the small circuit classes FAC⁰ and FTC⁰.

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Melissa Antonelli, Arnaud Durand, and Juha Kontinen. A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.10

Author Details

Melissa Antonelli
  • HIIT & University of Helsinki, Finland
Arnaud Durand
  • Université Paris Cité, France
Juha Kontinen
  • University of Helsinki, Finland

Funding

  • Antonelli, Melissa: Supported by HIIT and Maupertuis' SMR Programme, on behalf of the Institute Français in Helsinki, the French Embassy to Finland, the French Ministry of Higher Education, Research and Innovation in partnership with the Finnish Society for Science and Letters and the Finnish Academy of Sciences and Letters.
  • Durand, Arnaud: Supported by Maupertuis' SMR Programme.
  • Kontinen, Juha: Supported by the Academy of Finland grant 345634.

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