Skip to Main content Skip to Navigation
Conference papers

Inference of polynomial invariants for imperative programs: a farewell to Gröbner bases

David Cachera 1 Thomas Jensen 1 Arnaud Jobin 1 Florent Kirchner 2
1 CELTIQUE - Software certification with semantic analysis
IRISA-D4 - LANGAGE ET GÉNIE LOGICIEL, Inria Rennes – Bretagne Atlantique
2 LIST - Laboratoire d'Intégration des Systèmes et des Technologies
Abstract : We propose a static analysis for computing polynomial invariants for imperative programs. The analysis is derived from an abstract interpretation of a backwards semantics, and computes pre-conditions for equalities like g = 0 to hold at the end of execution. A distinguishing feature of the technique is that it computes polynomial loop invariants without resorting to Gröbner base computations. The analysis uses remainder computations over parameterized polynomials in order to handle conditionals and loops efficiently. The algorithm can analyse and find all loop invariants reported previously in the literature, and executes significantly faster than implementations using Gröbner bases.
Document type :
Conference papers
Complete list of metadata
https://hal.inria.fr/hal-00758890
Contributor : David Cachera <>
Submitted on : Thursday, November 29, 2012 - 3:11:51 PM
Last modification on : Friday, June 25, 2021 - 9:48:03 AM

Identifiers

  • HAL Id : hal-00758890, version 1

Collections

CNRS | INRIA | UNIV-RENNES1 | IRISA | IRISA-D4 | INSTITUT-TELECOM | CEA | DRT | UR1-UFR-ISTIC | LIST | UNIV-RENNES | INSA-RENNES

Citation

David Cachera, Thomas Jensen, Arnaud Jobin, Florent Kirchner. Inference of polynomial invariants for imperative programs: a farewell to Gröbner bases. SAS - 19th International Static Analysis Symposium - 2012, Sep 2012, Deauville, France. ⟨hal-00758890⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

1941

 

Contact                    Legal Notice                    Personal Data