# Numerical invariants through convex relaxation and max-strategy iteration

@article{Gawlitza2014NumericalIT, title={Numerical invariants through convex relaxation and max-strategy iteration}, author={Thomas Gawlitza and Helmut Seidl}, journal={Formal Methods in System Design}, year={2014}, volume={44}, pages={101-148} }

We present an algorithm for computing the uniquely determined least fixpoints of self-maps on $\overline{\mathbb{R}}^{n}$ (with $\overline{\mathbb{R}} = \mathbb{R} \cup\{ \pm\infty\}$) that are point-wise maximums of finitely many monotone and order-concave self-maps. This natural problem occurs in the context of systems analysis and verification. As an example application we discuss how our method can be used to compute template-based quadratic invariants for linear systems with guards. The…

## 3 Citations

Finding inductive invariants using satisfiability modulo theories and convex optimization. (Recherche d'invariants inductifs par satisfiabilité modulo théorie et optimisation convexe)

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A novel "formula slicing'' method for finding potentially disjunctive inductive invariants from program fragments obtained by symbolic execution is developed, and an algorithm parameterizable with any abstract interpretation for summary generation is developed and studied.

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- 2020

This work proposes a heuristic procedure based on simulation and counterexample-guided refinement that generates invariants of the form of a convex polynomial inequality that tightly bounds the values of loop variables that are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs.

Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs

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The technique developed is guaranteed to yield the strongest inductive invariant that can be expressed within the template linear constraint domain in use, and it is proved to have optimal complexity: the decision problem associated with the fixpoint problem is in the second level of the polynomial-time hierarchy.

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