Algebraic cell decomposition in NC

  • Authors:
  • Dexter Kozen;Chee-Kang Yap

  • Affiliations:
  • -;-

  • Venue:
  • SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1985

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Abstract

We give an algorithm to construct a cell decomposition of Rd, including adjacency information, defined by any given set of rational polynomials in d variables. The algorithm runs in single exponential parallel time, and in NC for fixed d. The algorithm extends a recent algorithm of Ben-Or, Kozen, and Reif for deciding the theory of real closed fields.