Abstract
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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© 1990 Springer-Verlag Berlin Heidelberg
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Dahlhaus, E. (1990). The complexity of subtheories of the existential linear theory of reals. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '89. CSL 1989. Lecture Notes in Computer Science, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52753-2_33
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DOI: https://doi.org/10.1007/3-540-52753-2_33
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