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Circuits versus Trees in Algebraic Complexity

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Abstract

This survey is devoted to some aspects of the “P = NP ?” problem over the real numbers and more general algebraic structures. We argue that given a structure M, it is important to find out whether NPM problems can be solved by polynomial depth computation trees, and if so whether these trees can be efficiently simulated by circuits. Point location, a problem of computational geometry, comes into play in the study of these questions for several structures of interest.

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Author information

Authors and Affiliations

  1. LIP, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69364, Lyon Cedex 07, France

    Pascal Koiran

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  1. Pascal Koiran
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Koiran, P. (2000). Circuits versus Trees in Algebraic Complexity. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_3

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  • DOI: https://doi.org/10.1007/3-540-46541-3_3

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  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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