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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 1106–1120 (Mi izv1566)  

This article is cited in 5 scientific papers (total in 5 papers)

The complexity of the decision problem for the first order theory of algebraically closed fields

D. Yu. Grigor'ev


Abstract: An algorithm is described that constructs, from every formula of the first order theory of algebraically closed fields, an equivalent quantifier-free formula in time which is polynomial in $\mathscr L^{n^{2a+1}}$, where $\mathscr L$ is the size of the formula, $n$ is the number of variables, and $a$ is the number of changes of quantifiers.
Bibliography: 15 titles.

Full text: PDF file (1775 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 459–475

Bibliographic databases:

UDC: 518.5
MSC: Primary 68Q40; Secondary 03C10, 12L99
Received: 25.07.1984

Citation: D. Yu. Grigor'ev, “The complexity of the decision problem for the first order theory of algebraically closed fields”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 1106–1120; Math. USSR-Izv., 29:2 (1987), 459–475

Citation in format AMSBIB
\Bibitem{Gri86}
\by D.~Yu.~Grigor'ev
\paper The complexity of the decision problem for the first order theory of algebraically closed fields
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 5
\pages 1106--1120
\mathnet{http://mi.mathnet.ru/izv1566}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=873663}
\zmath{https://zbmath.org/?q=an:0631.03006|0625.03004}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 459--475
\crossref{https://doi.org/10.1070/IM1987v029n02ABEH000979}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Noaï Fitchas, André Galligo, Jacques Morgenstern, “Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields”, Journal of Pure and Applied Algebra, 67:1 (1990), 1  crossref
    2. James Renegar, “On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals”, Journal of Symbolic Computation, 13:3 (1992), 255  crossref
    3. Gregorio Malajovich, Klaus Meer, “On the Structure of $\cal NP_\Bbb C$”, SIAM J Comput, 28:1 (1998), 27  crossref  mathscinet  zmath  isi
    4. Susana Puddu, Juan Sabia, “An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs”, Journal of Pure and Applied Algebra, 129:2 (1998), 173  crossref
    5. A. V. Seliverstov, “Kubicheskie formy bez monomov ot dvukh peremennykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 71–77  mathnet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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