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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2016.20
URN: urn:nbn:de:0030-drops-65601
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6560/
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Durand, Arnaud ; Haak, Anselm ; Kontinen, Juha ; Vollmer, Heribert

Descriptive Complexity of #AC^0 Functions

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LIPIcs-CSL-2016-20.pdf (0.5 MB)


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 #AC^0 appear as classes of this hierarchy. In this way, we unconditionally place #AC^0 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 #AC^0 which can be descriptively characterized as a class in our framework.

BibTeX - Entry

@InProceedings{durand_et_al:LIPIcs:2016:6560,
  author =	{Arnaud Durand and Anselm Haak and Juha Kontinen and Heribert Vollmer},
  title =	{{Descriptive Complexity of #AC^0 Functions}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6560},
  URN =		{urn:nbn:de:0030-drops-65601},
  doi =		{10.4230/LIPIcs.CSL.2016.20},
  annote =	{Keywords: finite model theory, Fagin's theorem, arithmetic circuits, counting classes, Skolem function}
}

Keywords: finite model theory, Fagin's theorem, arithmetic circuits, counting classes, Skolem function
Seminar: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 25.08.2016


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