A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations
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.
Implicit computational complexity
parallel computation
ordinary differential equations
circuit complexity
Theory of computation~Complexity classes
Theory of computation~Circuit complexity
10:1-10:18
Regular Paper
Melissa
Antonelli
Melissa Antonelli
HIIT & University of Helsinki, Finland
https://orcid.org/0009-0006-9072-4847
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.
Arnaud
Durand
Arnaud Durand
Université Paris Cité, France
https://orcid.org/0000-0003-2976-7259
Supported by Maupertuis' SMR Programme.
Juha
Kontinen
Juha Kontinen
University of Helsinki, Finland
https://orcid.org/0000-0003-0115-5154
Supported by the Academy of Finland grant 345634.
10.4230/LIPIcs.MFCS.2024.10
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Melissa Antonelli, Arnaud Durand, and Juha Kontinen
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