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Parametric equation solving and quantifier elimination in finite fields with the characteristic set method

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Abstract

For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametric values the system has solutions and at the same time presents the solutions in the form of proper chains. By the refined cover, the author gives a complete classification of the number of solutions for this system, that is, the author divides the parameter space into several disjoint components, and on every component the system has a fix number of solutions. Moreover, the author develops a method of quantifier elimination for first order formulas in finite fields.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100190, China

    Zhenyu Huang

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  1. Zhenyu Huang
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Correspondence to Zhenyu Huang.

Additional information

This work is supported by the National 973 Program of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 60970152.

This paper was recommended for publication by Editor Ziming LI.

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Huang, Z. Parametric equation solving and quantifier elimination in finite fields with the characteristic set method. J Syst Sci Complex 25, 778–791 (2012). https://doi.org/10.1007/s11424-012-0168-4

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  • DOI: https://doi.org/10.1007/s11424-012-0168-4

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