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A Note on Karr’s Algorithm

  • Markus Müller-Olm
  • Helmut Seidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We give a simple formulation of Karr’s algorithm for computing all affine relationships in affine programs. This simplified algorithm runs in time \(\mathcal{O}(nk^{3})\) where n is the program size and k is the number of program variables assuming unit cost for arithmetic operations. This improves upon the original formulation by a factor of k. Moreover, our re-formulation avoids exponential growth of the lengths of intermediately occurring numbers (in binary representation) and uses less complicated elementary operations. We also describe a generalization that determines all polynomial relations up to degree d in time \(\mathcal{O}(nk^{3d})\).

Keywords

Arithmetic Operation Complete Lattice Gaussian Elimination Program Variable Program Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Markus Müller-Olm
    • 1
  • Helmut Seidl
    • 2
  1. 1.FB Informatik, LG PI 5FernUniversität HagenHagenGermany
  2. 2.Informatik, I2TU MünchenMünchenGermany

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