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Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization

Abstract : While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The verification of user-provided properties is not easily compatible with the usual forward fixpoint computation using numerical abstract domains. We propose here to rely on sums-of-squares programming to characterize a property-driven polynomial invariant. This invariant generation can be guided by either boundedness, or in contrary, a given zone of the state space to avoid. While the target property is not necessarily inductive with respect to the program semantics, our method identifies a stronger inductive polynomial invariant using numerical optimization. Our method applies to a wide set of programs: a main while loop composed of a disjunction (if- then-else) of polynomial updates e.g. piecewise polynomial controllers. It has been evaluated on various programs.
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Preprints, Working Papers, ...
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Contributor : Pierre-Loïc Garoche <>
Submitted on : Tuesday, March 24, 2015 - 12:26:41 PM
Last modification on : Tuesday, March 16, 2021 - 3:44:17 PM
Long-term archiving on: : Wednesday, November 9, 2016 - 12:40:56 PM


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  • HAL Id : hal-01134816, version 1
  • ARXIV : 1503.07025



Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization. 2015. ⟨hal-01134816⟩



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