A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations
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| Titel: | A New Characterization of FAC⁰ via Discrete Ordinary Differential Equations |
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| Autoren: | Antonelli, Melissa, Durand, Arnaud, Kontinen, Juha |
| Weitere Verfasser: | Department of Computer Science, Helsinki Institute for Information Technology, Department of Mathematics and Statistics, Melissa Antonelli and Arnaud Durand and Juha Kontinen |
| Verlagsinformationen: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2024. |
| Publikationsjahr: | 2024 |
| Schlagwörter: | Small Circuit Classes, Discrete ODEs, Implicit computational complexity, Computer and information sciences, Implicit Computational Complexity, ordinary differential equations, ddc:004, parallel computation, Parallel Computation, circuit complexity |
| Beschreibung: | 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. |
| Publikationsart: | Conference object Article |
| Dateibeschreibung: | application/pdf |
| Sprache: | English |
| DOI: | 10.4230/lipics.mfcs.2024.10 |
| Zugangs-URL: | http://hdl.handle.net/10138/585925 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.10 |
| Rights: | CC BY |
| Dokumentencode: | edsair.dedup.wf.002..fa3ad1bb3a1bbd6ba9c0ec58f4c1f58b |
| Datenbank: | OpenAIRE |
Nájsť tento článok vo Web of Science | 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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| DOI: | 10.4230/lipics.mfcs.2024.10 |