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Verifying Nonlinear Real Formulas Via Sums of Squares

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Theorem Proving in Higher Order Logics (TPHOLs 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4732))

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Abstract

Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of equations and inequalities. A particularly attractive feature is that suitable ‘sum of squares’ certificates can be found by sophisticated numerical methods such as semidefinite programming, yet the actual verification of the resulting proof is straightforward even in a highly foundational theorem prover. We will describe our experience with an implementation in HOL Light, noting some successes as well as difficulties. We also describe a new approach to the univariate case that can handle some otherwise difficult examples.

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Authors and Affiliations

  1. Intel Corporation, JF1-13, 2111 NE 25th Avenue, Hillsboro OR 97124, USA

    John Harrison

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  1. John Harrison
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Klaus Schneider Jens Brandt

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Harrison, J. (2007). Verifying Nonlinear Real Formulas Via Sums of Squares. In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_9

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  • DOI: https://doi.org/10.1007/978-3-540-74591-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74590-7

  • Online ISBN: 978-3-540-74591-4

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