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Published in:
2015 | OriginalPaper | Chapter
A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets
Authors : Khalil Ghorbal, Andrew Sogokon, André Platzer
Published in: Verification, Model Checking, and Abstract Interpretation
Publisher: Springer Berlin Heidelberg
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This paper presents a theoretical and experimental comparison of sound proof rules for proving invariance of algebraic sets, that is, sets satisfying polynomial equalities, under the flow of polynomial ordinary differential equations. Problems of this nature arise in formal verification of continuous and hybrid dynamical systems, where there is an increasing need for methods to expedite formal proofs. We study the trade-off between proof rule generality and practical performance and evaluate our theoretical observations on a set of heterogeneous benchmarks. The relationship between increased deductive power and running time performance of the proof rules is far from obvious; we discuss and illustrate certain classes of problems where this relationship is interesting.