Generating polynomial invariants with DISCOVERER and QEPCAD

Authors:
Yinghua Chen;Bican Xia;Lu Yang;Naijun Zhan
Affiliations:
LMAM & School of Mathematical Sciences, Peking University;LMAM & School of Mathematical Sciences, Peking University;Institute of Theoretical Computing, East China Normal University;Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Zhong Guan Cun, Beijing, P.R. China
Venue:
Formal methods and hybrid real-time systems
Year:
2007

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Abstract

This paper investigates howto apply the techniques on solving semi-algebraic systems to invariant generation of polynomial programs. By our approach, the generated invariants represented as a semi-algebraic system are more expressive than those generated with the well-established 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 QEPCAD1.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.