research-article

From post-conditions to post-region invariants: deductive verification of hybrid objects

Author:

Eduard KamburjanAuthors Info & Claims

HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control

Article No.: 9, Pages 1 - 11

https://doi.org/10.1145/3447928.3456633

Published: 19 May 2021 Publication History

Abstract

We introduce a new system for object-oriented distributed hybrid systems to verify object invariants and method contracts. In a hybrid setting, the object invariant must not only be the post-condition of a method, but also has to hold in the post-region of a method, because the state of the object evolves according to continuous dynamics. The post-region describes all reachable states after method termination before another process runs. This set can be approximated using lightweight analysis of the class structure. The system naturally generalizes rely-guarantee reasoning of discrete object-oriented languages to hybrid systems and carries over its compositionality to hybrid systems: only one dL-proof obligation is generated per method. By reasoning about the minimal size of the post-region, local Zeno behavior can also be analyzed. Our approach is implemented for the Hybrid Active Object language HABS.

References

[1]

Wolfgang Ahrendt, Bernhard Beckert, Richard Bubel, Reiner Hähnle, Peter H. Schmitt, and Mattias Ulbrich (Eds.). 2016. Deductive Software Verification - The KeY Book - From Theory to Practice. LNCS, Vol. 10001. Springer.

[2]

Elvira Albert, Frank S. de Boer, Reiner Hähnle, Einar Broch Johnsen, Rudolf Schlatte, Silvia Lizeth Tapia Tarifa, and Peter Y. H. Wong. 2014. Formal modeling and analysis of resource management for cloud architectures: an industrial case study using Real-Time ABS. Service Oriented Computing and Applications 8, 4 (2014), 323--339.

Digital Library

[3]

Rajeev Alur, Costas Courcoubetis, Nicolas Halbwachs, Thomas A. Henzinger, Pei-Hsin Ho, Xavier Nicollin, Alfredo Olivero, Joseph Sifakis, and Sergio Yovine. 1995. The Algorithmic Analysis of Hybrid Systems. Theor. Comput. Sci. 138, 1 (1995), 3--34.

Digital Library

[4]

Nikolaos Bezirgiannis, Frank S. de Boer, Einar Broch Johnsen, Ka I Pun, and Silvia Lizeth Tapia Tarifa. 2019. Implementing SOS with Active Objects: A Case Study of a Multicore Memory System. In FASE 2019 (LNCS, Vol. 11424), Reiner Hähnle and Wil M. P. van der Aalst (Eds.). Springer, 332--350.

[5]

Joakim Bjørk, Frank S. de Boer, Einar Broch Johnsen, Rudolf Schlatte, and Silvia Lizeth Tapia Tarifa. 2013. User-defined schedulers for real-time concurrent objects. Innovations in Systems and Software Engineering 9, 1 (2013), 29--43.

Digital Library

[6]

Frank S. de Boer, Vlad Serbanescu, Reiner Hähnle, Ludovic Henrio, Justine Rochas, Crystal Chang Din, Einar Broch Johnsen, Marjan Sirjani, Ehsan Khamespanah, Kiko Fernandez-Reyes, and Albert Mingkun Yang. 2017. A Survey of Active Object Languages. Comput. Surveys 50, 5 (2017), 1--39.

Digital Library

[7]

Alexandre Donzé and Goran Frehse. 2013. Modular, hierarchical models of control systems in SpaceEx. In ECC 2013. IEEE, 4244--4251.

[8]

Antonio Flores-Montoya. 2016. Upper and Lower Amortized Cost Bounds of Programs Expressed as Cost Relations. In FM 2016 (LNCS, Vol. 9995), John S. Fitzgerald, Constance L. Heitmeyer, Stefania Gnesi, and Anna Philippou (Eds.). 254--273.

[9]

G. Frehse, Zhi Han, and B. Krogh. 2004. Assume-guarantee reasoning for hybrid I/O-automata by over-approximation of continuous interaction. In CDC 2004, Vol. 1. 479--484 Vol.1.

[10]

Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Völp, and André Platzer. 2015. KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems. In CADE'25 (LNCS, Vol. 9195). Springer, 527--538.

[11]

Sergey Goncharov and Renato Neves. 2019. An Adequate While-Language for Hybrid Computation. CoRR abs/1902.07684 (2019).

[12]

Daniel Grahl, Richard Bubel, Wojciech Mostowski, Peter H. Schmitt, Mattias Ulbrich, and Benjamin Weiß. 2016. Modular Specification and Verification. In The KeY Book. LNCS, Vol. 10001. Springer.

[13]

David Harel, Jerzy Tiuryn, and Dexter Kozen. 2000. Dynamic Logic. MIT Press.

Digital Library

[14]

Ichiro Hasuo and Kohei Suenaga. 2012. Exercises in Nonstandard Static Analysis of Hybrid Systems. In CAV 2012 (LNCS, Vol. 7358), P. Madhusudan and Sanjit A. Seshia (Eds.). Springer, 462--478.

Digital Library

[15]

Ludovic Henrio, Cosimo Laneve, and Vincenzo Mastandrea. 2017. Analysis of Synchronisations in Stateful Active Objects. In Integrated Formal Methods, Nadia Polikarpova and Steve Schneider (Eds.). Springer, 195--210.

[16]

Thomas A. Henzinger, Marius Minea, and Vinayak S. Prabhu. 2001. Assume-Guarantee Reasoning for Hierarchical Hybrid Systems. In HSCC 2001 (LNCS, Vol. 2034), Maria Domenica Di Benedetto and Alberto L. Sangiovanni-Vincentelli (Eds.). Springer, 275--290.

[17]

Iman Jahandideh, Fatemeh Ghassemi, and Marjan Sirjani. 2019. Hybrid Rebeca: Modeling and Analyzing of Cyber-Physical Systems. CoRR abs/1901.02597 (2019). arXiv:1901.02597

[18]

Eduard Kamburjan. 2018. Detecting Deadlocks in Formal System Models with Condition Synchronization. ECEASST 76 (2018).

[19]

Eduard Kamburjan. 2019. Behavioral Program Logic. In TABLEAUX 2019 (LNCS, Vol. 11714), Serenella Cerrito and Andrei Popescu (Eds.). Springer, 391--408.

[20]

Eduard Kamburjan, Crystal Chang Din, Reiner Hähnle, and Einar Broch Johnsen. 2020. Behavioral Contracts for Cooperative Scheduling. In Deductive Verification: The State of the Future, Wolfgang Ahrendt, Bernhard Beckert, Richard Bubel, Reiner Hähnle, and Mattias Ulbrich (Eds.). LNCS, Vol. 12345. Springer.

[21]

Eduard Kamburjan, Reiner Hähnle, and Sebastian Schön. 2018. Formal modeling and analysis of railway operations with active objects. Sci. Comput. Program. 166 (2018), 167--193.

[22]

Eduard Kamburjan, Stefan Mitsch, Martina Kettenbach, and Reiner Hähnle. 2019. Modeling and Verifying Cyber-Physical Systems with Hybrid Active Objects. CoRR abs/1906.05704 (2019).

[23]

Simon Lunel, Benoît Boyer, and Jean-Pierre Talpin. 2017. Compositional Proofs in Differential Dynamic Logic dL. In ACSD'17. IEEE Computer Society, 19--28.

[24]

Simon Lunel, Stefan Mitsch, Benoît Boyer, and Jean-Pierre Talpin. 2019. Parallel Composition and Modular Verification of Computer Controlled Systems in Differential Dynamic Logic. In FM (LNCS, Vol. 11800), Maurice H. ter Beek, Annabelle McIver, and José N. Oliveira (Eds.). Springer, 354--370.

Digital Library

[25]

Nancy A. Lynch, Roberto Segala, and Frits W. Vaandrager. 2003. Hybrid I/O automata. Inf. Comput. 185, 1 (2003), 105--157.

Digital Library

[26]

Bertrand Meyer. 1992. Applying "Design by Contract". IEEE Computer 25, 10 (Oct. 1992), 40--51.

Digital Library

[27]

Andreas Müller, Stefan Mitsch, Werner Retschitzegger, Wieland Schwinger, and André Platzer. 2018. Tactical Contract Composition for Hybrid System Component Verification. STTT 20, 6 (2018), 615--643.

[28]

André Platzer. 2010. Differential-algebraic Dynamic Logic for Differential-algebraic Programs. J. of Logic and Computation 20, 1 (2010), 309--352.

Digital Library

[29]

André Platzer. 2010. Quantified Differential Dynamic Logic for Distributed Hybrid Systems. In CSL 2010 (LNCS, Vol. 6247). Springer, 469--483.

[30]

André Platzer. 2012. A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems. LMCS 8, 4 (2012), 1--44.

[31]

André Platzer. 2012. The Complete Proof Theory of Hybrid Systems. In LICS. IEEE, 541--550.

[32]

André Platzer. 2017. A Complete Uniform Substitution Calculus for Differential Dynamic Logic. J. Automated Reasoning 59, 2 (2017), 219--265.

Digital Library

[33]

André Platzer. 2018. Logical Foundations of Cyber-Physical Systems. Springer.

Digital Library

[34]

Kohei Suenaga and Ichiro Hasuo. 2011. Programming with Infinitesimals: A While-Language for Hybrid System Modeling. In ICALP (2) (LNCS, Vol. 6756). Springer, 392--403.

[35]

Stavros Tripakis. 1999. Verifying Progress in Timed Systems. In ARTS (Lecture Notes in Computer Science, Vol. 1601). Springer, 299--314.

Cited By

Chen Jde Mendonça JAyele BBekele BJalili SSharma PWohlfeil NZhang YJeannin J(2024)Synchronous Programming with Refinement TypesProceedings of the ACM on Programming Languages10.1145/36746578:ICFP(938-972)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674657
Platzer A(2024)Hybrid Dynamical Systems Logic and Its RefinementsScience of Computer Programming10.1016/j.scico.2024.103179(103179)Online publication date: Jul-2024
https://doi.org/10.1016/j.scico.2024.103179
Kamburjan EPferscher ASchlatte RSieve RTarifa SJohnsen E(2024)Semantic Reflection and Digital Twins: A Comprehensive OverviewThe Combined Power of Research, Education, and Dissemination10.1007/978-3-031-73887-6_11(129-145)Online publication date: 23-Oct-2024
https://doi.org/10.1007/978-3-031-73887-6_11
Show More Cited By

Index Terms

From post-conditions to post-region invariants: deductive verification of hybrid objects
1. Theory of computation

Recommendations

Deductive verification of active objects with Crowbar▪
Abstract
We present Crowbar, a deductive verification tool for the Active Object language ABS. Crowbar implements novel specification approaches specifically for distributed systems. For user interaction, counterexamples are presented as ...
Reusable Specification Patterns for Verification of Resilience in Autonomous Hybrid Systems
Formal Methods
Abstract
Autonomous hybrid systems are systems that combine discrete and continuous behavior with autonomous decision-making, e.g., using reinforcement learning. Such systems are increasingly used in safety-critical applications such as self-driving cars, ...
A Compositional Modelling and Verification Framework for Stochastic Hybrid Systems
Abstract
In this paper, we propose a general compositional approach for modelling and verification of stochastic hybrid systems (SHSs). We extend Hybrid CSP (HCSP), a very expressive process algebra-like formal modeling language for hybrid systems, by ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control

May 2021

300 pages

ISBN:9781450383394

DOI:10.1145/3447928

Program Chairs:
Sergiy Bogomolov
Newcastle University, UK
,
Raphaël Jungers
UCLouvain, Belgium

Copyright © 2021 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

SIGBED: ACM Special Interest Group on Embedded Systems

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 May 2021

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Badges

Results Reproduced / v1.1

Author Tags

Qualifiers

Research-article

Conference

HSCC '21

Sponsor:

SIGBED

HSCC '21: 24th ACM International Conference on Hybrid Systems: Computation and Control

May 19 - 21, 2021

Tennessee, Nashville

Acceptance Rates

HSCC '21 Paper Acceptance Rate 27 of 77 submissions, 35%;

Overall Acceptance Rate 153 of 373 submissions, 41%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

5
Total Citations
View Citations
139
Total Downloads

Downloads (Last 12 months)12
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Chen Jde Mendonça JAyele BBekele BJalili SSharma PWohlfeil NZhang YJeannin J(2024)Synchronous Programming with Refinement TypesProceedings of the ACM on Programming Languages10.1145/36746578:ICFP(938-972)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674657
Platzer A(2024)Hybrid Dynamical Systems Logic and Its RefinementsScience of Computer Programming10.1016/j.scico.2024.103179(103179)Online publication date: Jul-2024
https://doi.org/10.1016/j.scico.2024.103179
Kamburjan EPferscher ASchlatte RSieve RTarifa SJohnsen E(2024)Semantic Reflection and Digital Twins: A Comprehensive OverviewThe Combined Power of Research, Education, and Dissemination10.1007/978-3-031-73887-6_11(129-145)Online publication date: 23-Oct-2024
https://doi.org/10.1007/978-3-031-73887-6_11
Kamburjan ELienhardt M(2024)Type-Based Verification of Delegated Control in Hybrid SystemsActive Object Languages: Current Research Trends10.1007/978-3-031-51060-1_12(323-358)Online publication date: 29-Jan-2024
https://doi.org/10.1007/978-3-031-51060-1_12
Kamburjan ESchlatte RJohnsen ETapia Tarifa S(2020)Designing Distributed Control with Hybrid Active ObjectsLeveraging Applications of Formal Methods, Verification and Validation: Tools and Trends10.1007/978-3-030-83723-5_7(88-108)Online publication date: 20-Oct-2020
https://dl.acm.org/doi/10.1007/978-3-030-83723-5_7

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten