Elsevier

Journal of Complexity

Volume 13, Issue 2, June 1997, Pages 279-300
Journal of Complexity

Regular Article
Real Data—Integer Solution Problems within the Blum–Shub–Smale Computational Model

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Abstract

This paper presents results connected with the theory of computation over the reals, developed recently by Blum, Shub, and Smale. The subjects of our investigation are variations of the well known Integer Linear Programming Problem and the Linear Diophantine Equation, where the coefficients are real numbers and we look for an integer solution. We show some results concerning the solvability and complexity of these problems, and we develop algorithms for their solution in the presence of additional information.

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E. SpeckerV. Strassen, Eds.

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This author is now with IMC-CNR, Via S. Maria, 46, 56100 Pisa, Italy; E-mail: [email protected]. Part of this work has been done while the author was visiting IMC-CNR and supported by a CNR fellowship.