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“…Abstract interpretation based techniques either ignore [15,22] or restrict conditions on branches to equalities or dis-equalities [17,6,21,4]. The techniques of [6,21,22,15] use Gröbner bases computations and [17] has no upper complexity bound.…”

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“…Abstract interpretation based techniques either ignore [15,22] or restrict conditions on branches to equalities or dis-equalities [17,6,21,4]. The techniques of [6,21,22,15] use Gröbner bases computations and [17] has no upper complexity bound.…”

“…The techniques of [6,21,22,15] use Gröbner bases computations and [17] has no upper complexity bound. Cachera et al [4] provide an algorithm that does not use Gröbner bases but interprets variables as taking values over the real numbers.…”

“…Existing sound tools for non-linear invariant generation can produce invariants that are conjunctions of polynomial equalities [51,38,50,14,46,53,17]. However, by imposing strict restrictions on syntax (such as no nested loops) [51,38] do not need to assume the degree of polynomials as the input.…”

“…However, by imposing strict restrictions on syntax (such as no nested loops) [51,38] do not need to assume the degree of polynomials as the input. Bagnara et al [4] introduce new variables for monomials and generate linear invariants over them by abstract interpretation over convex polyhedra.…”