Verifying Nonlinear Real Formulas Via Sums of Squares

  • John Harrison
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4732)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

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

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