Generating Polynomial Invariants with DISCOVERER and QEPCAD

This paper investigates how to apply the techniques on solving semi-algebraic systems to invariant generation of polynomial programs. By our approach, the generated invariants represented as a semialgebraic system are more expressive than those generated with the wellestablished approaches in the literature, which are normally represented as a conjunction of polynomial equations. We implement this approach with the computer algebra tools DISCOVERER and QEPCAD. We also explain, through the complexity analysis, why our approach is more efficient and practical than the one of [17] which directly applies first-order quantifier elimination. keywords Program Verification, Invariant Generation, Polynomial Programs, Semi-Algebraic Systems; Quantifier Elimination, DISCOVERER, QEPCAD