Polynomial invariants by linear algebra

TL;DR

This paper introduces a new linear algebra-based method for generating polynomial invariants in program analysis, combining polynomial reduction and linear loop invariants with polynomial complexity.

Contribution

It presents a novel technique that reduces polynomial assignments to linear loops and generates inductive invariants, ensuring completeness for bounded degrees.

Findings

Polynomial complexity for a bounded number of variables

Complete for bounded degree polynomial invariants

Successfully implemented for C program verification

Abstract

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.