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Algebraic Complexity Classes

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Perspectives in Computational Complexity

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 26))

Abstract

This survey describes, at an introductory level, the algebraic complexity framework originally proposed by Leslie Valiant in 1979, and some of the insights that have been obtained more recently.

The idea for writing this survey came while the author was working on the Indo-French CEFIPRA-supported project 4702-1.

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Acknowledgments

I thank Arvind and Manindra for inviting me to contribute to this volume in honour of Somenath Biswas, a wonderful professional colleague and friend. I thank CEFIPRA for supporting an Indo-French collaboration (project 4702-1); many of my ideas for how to present this survey were crystallised during my visit to University of Paris-Diderot during May–June 2012. I have picked material I found interesting, and have not really attempted an exhaustive coverage. I apologise in advance to those whose favourite results I have omitted. I gratefully acknowledge many insightful discussions with Eric Allender, V. Arvind, Hervé Fournier, Bruno Grenet, Nutan Limaye, Guillaume Malod, Stefan Mengel, Sylvain Perifel, B. V. Raghavendra Rao, Nitin Saurabh, Karteek Sreenivasaiah, Srikanth Srinivasan, V. Vinay. I thank the organisers of the Dagstuhl Seminars on Circuits, Logic and Games (Feb 2010) and Computational Counting (Dec 2010) for inviting me and giving me the opportunity to discuss these topics. The survey by Pascal Koiran at the Dagstuhl seminar on Computational Counting in Dec 2010 was particularly helpful.

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  1. The Institute of Mathematical Sciences, CIT Campus, Chennai, 600113, India

    Meena Mahajan

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  1. Meena Mahajan
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  1. Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India, Kanpur, India

    Manindra Agrawal

  2. CIT Campus, Institute of Mathematical Sciences, Chennai, India

    Vikraman Arvind

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Mahajan, M. (2014). Algebraic Complexity Classes. In: Agrawal, M., Arvind, V. (eds) Perspectives in Computational Complexity. Progress in Computer Science and Applied Logic, vol 26. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05446-9_4

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