The complexity of subtheories of the existential linear theory of reals

  • Elias Dahlhaus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 440)


The linear theory consists of all sentences of signatur (0,1,+,<,k·_, k is a rational number) true in the model of real numbers. We shall prove that the existential linear theory of real numbers restricted to a quantifier free part of Krom formulas is NP-complete even for some restrictions on the structure of atoms.

In the case that the quantifier free part is a conjunction of atomic formulas we have nothing else than the linear optimation problem, which is P-complete. In the case of two variables per atomic formula the problem is in NC.

Also the case that all atoms are of the form Σ i a i x i c, such that c>0, is considered.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Elias Dahlhaus
    • 1
  1. 1.Dept. of Computer ScienceUniversity of BonnGermany

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