Descriptive complexity of #AC0 functions

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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

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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.
License of this version: CC BY 3.0
Document Type: article
Publishing status: publishedVersion
Issue Date: 2016
Appears in Collections:Fakultät für Elektrotechnik und Informatik

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pos. country downloads
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1 image of flag of Germany Germany 23 92.00%
2 image of flag of United States United States 1 4.00%
3 image of flag of Russian Federation Russian Federation 1 4.00%

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