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Pegasus: a framework for sound continuous invariant generation

Pegasus: a framework for sound continuous invariant generation
Pegasus: a framework for sound continuous invariant generation
Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loops forever, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to automation of formal proofs of safety in hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.
invariant generation, formal verification, theorem proving, continuous systems, hybrid systems, continuous invariants
0302-9743
138-157
Springer
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Mitsch, Stefan
ce963ace-2873-49b3-a5e9-a7549a4804c0
Tan, Yong Kiam
09ebcf1a-92e4-4b3b-9d57-b08934e67b0a
Cordwell, Katherine
04f43f61-6331-4b94-918e-a0e1a045cdeb
Platzer, André
8886030f-8d61-4d2f-a5b2-24f92c1b2a2c
M., ter Beek
A., McIver
J., Oliveira
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Mitsch, Stefan
ce963ace-2873-49b3-a5e9-a7549a4804c0
Tan, Yong Kiam
09ebcf1a-92e4-4b3b-9d57-b08934e67b0a
Cordwell, Katherine
04f43f61-6331-4b94-918e-a0e1a045cdeb
Platzer, André
8886030f-8d61-4d2f-a5b2-24f92c1b2a2c
M., ter Beek
A., McIver
J., Oliveira

Sogokon, Andrew, Mitsch, Stefan, Tan, Yong Kiam, Cordwell, Katherine and Platzer, André (2019) Pegasus: a framework for sound continuous invariant generation. M., ter Beek, A., McIver and J., Oliveira (eds.) In Formal Methods – The Next 30 Years: Third World Congress, FM 2019, Portugal, October 7–11, 2019, Proceedings. vol. 11800, Springer. pp. 138-157 . (doi:10.1007/978-3-030-30942-8_10).

Record type: Conference or Workshop Item (Paper)

Abstract

Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loops forever, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to automation of formal proofs of safety in hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.

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fm-2019-pegasus-continuous-invariant-generator - Accepted Manuscript
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Accepted/In Press date: 12 June 2019
e-pub ahead of print date: 23 September 2019
Published date: 2019
Keywords: invariant generation, formal verification, theorem proving, continuous systems, hybrid systems, continuous invariants

Identifiers

Local EPrints ID: 433821
URI: http://eprints.soton.ac.uk/id/eprint/433821
ISSN: 0302-9743
PURE UUID: da7caceb-27b8-4a43-882b-8fe8a32f3f89

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Date deposited: 04 Sep 2019 16:30
Last modified: 06 Oct 2020 17:53

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Contributors

Author: Andrew Sogokon
Author: Stefan Mitsch
Author: Yong Kiam Tan
Author: Katherine Cordwell
Author: André Platzer
Editor: ter Beek M.
Editor: McIver A.
Editor: Oliveira J.

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