Inference of Polynomial Invariants for Imperative Programs: A Farewell to Gröbner Bases

  • David Cachera
  • Thomas Jensen
  • Arnaud Jobin
  • Florent Kirchner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7460)


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 a large majority of loop invariants reported previously in the literature, and executes significantly faster than implementations using Gröbner bases.


Base Computation Abstract Interpretation Polynomial Invariant Abstract Domain Abstract Semantic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David Cachera
    • 1
  • Thomas Jensen
    • 2
  • Arnaud Jobin
    • 3
  • Florent Kirchner
    • 4
  1. 1.ENS Cachan Bretagne, IRISARennesFrance
  2. 2.Inria Rennes - Bretagne AtlantiqueFrance
  3. 3.Université Rennes 1, IRISARennesFrance
  4. 4.CEA, LISTGif-sur-YvetteFrance

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