Polynomial invariants by linear algebra

S. De Oliveira (1) , S. Bensalem (2) , V. Prevosto (1)

1 DILS - Département Ingénierie Logiciels et Systèmes
2 UGA [2016-2019] - Université Grenoble Alpes [2016-2019]

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.

Keywords: C (programming language); Linear algebra; Bounded degree; C programs; Certain hypothesis; Generating polynomial; Polynomial complexity; Polynomial invariants; Polynomials

Domains: Computer Science [cs]

S. De Oliveira, S. Bensalem, V. Prevosto. Polynomial invariants by linear algebra. Lecture Notes in Computer Science, 2016, 9938 LNCS, pp.479-494. ⟨10.1007/978-3-319-46520-3_30⟩. ⟨cea-01808891⟩