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Recent advances in automated theorem proving on inequalities

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Abstract

Automated theorem proving on inequalities is always considered as a difficult topic in the area of automated reasoning. The relevant algorithms depend fundamentally on real algebra and real geometry, and the computational complexity increases very quickly with the dimension, that is, the number of parameters. Some well-known algorithms are complete theoretically but inefficient in practice, which cannot verify non-trivial propositions in batches. A dimension-decreasing algorithm presented here can treat radicals efficiently and make the dimensions the lowest. Based upon this algorithm, a generic program called “BOTTEMA” was implemented on a personal computer. More than 1000 algebraic and geometric inequalities including hundreds of open problems have been verified in this way. This makes it possible to check a finite many inequalities instead of solving a global-optimization problem.

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Authors and Affiliations

  1. Chengdu Institute of Computer Applications, Chinese Academy of Sciences, 610041, Chengdu, P.R. China

    Yang Lu

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  1. Yang Lu
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Correspondence to Yang Lu.

Additional information

Research supported in part by National ‘973’ Project of China and ‘95’ Key Project on Fundamental Research of Academia Sinica.

Yang Lu received his diploma in mathematics from Peking University in 1959. He is a Professor in computer science at Chengdu Institute of Computer Applications, Chinese Academy of Sciences. His major research interests include automated theorem proving, symbolic computation and intelligent software technology.

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Yang, L. Recent advances in automated theorem proving on inequalities. J. Comput. Sci. & Technol. 14, 434–446 (1999). https://doi.org/10.1007/BF02948785

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