Durand, A.; Haak, A.; Kontinen, J.; Vollmer, H.: Descriptive complexity of #AC0 functions. In: Leibniz International Proceedings in Informatics, LIPIcs 62 (2016). DOI:
https://doi.org/10.4230/LIPIcs.CSL.2016.20
Abstract: |
We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely determine the inclusion structure and show that #P and #AC0 appear as classes of this hierarchy. In this way, we unconditionally place #AC0 properly in a strict hierarchy of arithmetic classes within #P. We compare our classes with a hierarchy within #P defined in a model-theoretic way by Saluja et al. We argue that our approach is better suited to study arithmetic circuit classes such as #AC0 which can be descriptively characterized as a class in our framework.
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License of this version: |
CC BY 3.0 Unported - https://creativecommons.org/licenses/by/3.0
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Publication type: |
Article |
Publishing status: |
publishedVersion |
Publication date: |
2016 |
Keywords english: |
Arithmetic circuits, Counting classes, Fagin's theorem, Finite model theory, Skolem function, Computational complexity, Logic circuits, Arithmetic circuit, Arithmetic computations, Counting class, Descriptive complexity, Fagin's theorem, Finite model theory, Function variables, Inclusion structure, Computer circuits
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DDC: |
004 | Informatik, 510 | Mathematik
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Controlled keywords(GND): |
Konferenzschrift
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