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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Contributeur : Pierre-Loïc Garoche <>
Soumis le : mardi 24 mars 2015 - 12:26:41
Dernière modification le : samedi 29 décembre 2018 - 18:20:02
Document(s) archivé(s) le : mercredi 9 novembre 2016 - 12:40:56


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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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