Abstract
This paper proposed an approach to automatically generate non-linear loop invariants.An invariant of a loop was hypothesized as a parameterized polynomial.Based on the inductive assertion's properties,we reduced the non-linear loop invariant problem to a numerical constraint solving problem.All the solutions to these constraints were the non-linear loop invariants of the program.The approach has been implemented in Maple.The implementation has been used to automatically discover nontrivial invariants for many programs.
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