A hierarchy of proof rules for checking positive invariance of algebraic and semi-algebraic sets

Abstract : This paper studies sound proof rules for checking positive invariance of algebraic and semi-algebraic sets, that is, sets satisfying polynomial equalities and those satisfying finite boolean combinations of polynomial equalities and inequalities, 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 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.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01232288
Contributor : Khalil Ghorbal <>
Submitted on : Monday, November 23, 2015 - 9:58:34 PM
Last modification on : Friday, September 13, 2019 - 9:48:42 AM
Long-term archiving on : Friday, April 28, 2017 - 6:47:49 PM

File

root.pdf
Files produced by the author(s)

Licence


Copyright

Identifiers

Citation

Khalil Ghorbal, Andrew Sogokon, André Platzer. A hierarchy of proof rules for checking positive invariance of algebraic and semi-algebraic sets. Computer Languages, Systems and Structures, Elsevier, 2017, Special issue on the 16th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI 2015), 47 (1), pp.19-43. ⟨10.1016/j.cl.2015.11.003⟩. ⟨hal-01232288⟩

Share

Metrics

Record views

661

Files downloads

612