arXiv subjects

Steven de Oliveira

Publications and source records attributed to Steven de Oliveira.

3 recordsLinked to original sources

arXiv2018

Left-eigenvectors are certificates of the Orbit Problem

This paper investigates the connexion between the Kannan-Lipton Orbit Problem and the polynomial invariant generator algorithm PILA based on eigenvectors computation. Namely, we reduce the problem of generating linear and polynomial certificates of non-reachability for the Orbit Problem for linear transformations with rational coefficients to the generalized eigenvector problem. Also, we prove the existence of such certificates for any transformation with integer coefficients, which is not the case with rational coefficients.

cs.LO↗

arXiv2016

Polynomial invariants by linear algebra

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.

cs.LO↗

arXiv2016

Synthesizing invariants by solving solvable loops

When proving invariance properties of a program, we face two problems. The first problem is related to the necessity of proving tautologies of considered assertion language, whereas the second manifests in the need of finding sufficiently strong invariants. This paper focuses on the second problem and describes a new method for the automatic generation of loop invariants that handles polynomial and non deterministic assignments. This technique is based on the eigenvector generation for a given linear transformation and on the polynomial optimization problem, which we implemented in the open-source tool Pilat.

cs.LO↗