LIPIcs.CSL.2017.5.pdf
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Arithmetic Circuits: An Overview (Invited Talk)
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26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2017-08-16
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Meena Mahajan. Arithmetic Circuits: An Overview (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 5:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CSL.2017.5
https://doi.org/10.4230/LIPIcs.CSL.2017.5
Abstract
This talk reviews recent developments in algebraic complexity
theory. It outlines some major results concerning structure,
completeness, closure, and lower bounds. It describes some techniques
that have been central to obtaining these results, including extreme
depth reduction, partial derivatives, and padding.
Keywords
- algebraic complexity
- circuits
- formulas
- branching programs
- determinant
- permanent
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References
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M. Mahajan. Algebraic complexity classes. In Perspectives in Computational Complexity: The Somenath Biswas Anniversary Volume, pages 51-75. Birkhäuser, 2014.
- Meena Mahajan and Nitin Saurabh. Some complete and intermediate polynomials in algebraic complexity theory. Thory of Computing Systems, page to appear, 2017. (CSR special issue). URL: http://dx.doi.org/10.1007/s00224-016-9740-y.
- Ramprasad Saptharishi. A survey of known lower bounds in arithmetic circuits. A continuously updated git survey. URL: https://github.com/dasarpmar/lowerbounds-survey.
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Amir Shpilka and Amir Yehudayoff. Arithmetic circuits: A survey of recent results and open questions. Foundations and Trends in Theoretical Computer Science, 5(3-4):207-388, 2010.