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.
@InProceedings{antonelli_et_al:LIPIcs.MFCS.2024.10, author = {Antonelli, Melissa and Durand, Arnaud and Kontinen, Juha}, title = {{A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {10:1--10:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.10}, URN = {urn:nbn:de:0030-drops-205664}, doi = {10.4230/LIPIcs.MFCS.2024.10}, annote = {Keywords: Implicit computational complexity, parallel computation, ordinary differential equations, circuit complexity} }
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