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Qualitative theorem proving in linear constraints

Chandru, Vijay and Lassez, Jean-Louis (2004) Qualitative theorem proving in linear constraints. In: Verification: Theory And Practice - Essays Dedicated To Zhoar Manna On The Occasion Of His 64th Birthday Book Series: Lecture Notes In Computer Science, 2772 . pp. 398-399.

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Abstract

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 04 Nov 2009 10:56
Last Modified: 19 Sep 2010 04:56
URI: http://eprints.iisc.ernet.in/id/eprint/17291

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