# Polynomial invariants by linear algebra

arXiv: https://arxiv.org/abs/1611.07726 · HTML: https://mlsanity.com/paper/1611.07726/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2016.

## Built on by (most cited first, 1 of 1)

- [Enhancing Automated Loop Invariant Generation for Complex Programs with Large Language Models](https://mlsanity.com/paper/2412.10483/) (2024)

## Abstract (arXiv)

We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a procedure for generating inductive invariants for linear loops. Both of these techniques have a polynomial complexity for a bounded number of variables and we guarantee the completeness of the technique for a bounded degree which we successfully implemented for C programs verification.