A fairness-based refinement strategy to transform liveness properties in Event-B models
A fairness-based refinement strategy to transform liveness properties in Event-B models
Stepwise development supported by the Event-B formalism has been used in the domain of system design and verification. This refinement approach guarantees that safety properties are preserved with Event-B proof obligations, while additional reasoning and fairness assumptions are required to prove the transformation of liveness properties in Event-B models. This paper presents a new proof-based approach that integrates Linear Temporal Logic (LTL) and Event-B for reasoning about the refinement of liveness properties. We first developed an extended version of LTL that could be used in Event-B models with three basic atomic propositions: state-related propositions, event-related propositions, and enabledness of events. Then we employed this extended LTL to express four important temporal properties with Event-B proof obligations and fairness assumptions. Besides the typical Event-B proof obligations, we specified conditions such as relative deadlock freeness, conditional convergence, and fairness assumptions to allow temporal properties to be transformed during refinement steps. The generic fairness-based refinement strategies were developed to replace or strengthen the fairness assumptions in the refinement steps of Event-B models. A reliable retransmission example is used to illustrate the approach.
Event-B, Fairness assumptions, Linear temporal logic, Refinement
Zhu, Chenyang
bb823fac-bd18-42a3-9720-6188fe84aca6
Butler, Michael
54b9c2c7-2574-438e-9a36-6842a3d53ed0
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Hoang, Son
dcc0431d-2847-4e1d-9a85-54e4d6bab43f
January 2023
Zhu, Chenyang
bb823fac-bd18-42a3-9720-6188fe84aca6
Butler, Michael
54b9c2c7-2574-438e-9a36-6842a3d53ed0
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Hoang, Son
dcc0431d-2847-4e1d-9a85-54e4d6bab43f
Zhu, Chenyang, Butler, Michael, Cirstea, Corina and Hoang, Son
(2023)
A fairness-based refinement strategy to transform liveness properties in Event-B models.
Science of Computer Programming, 225, [102907].
(doi:10.1016/j.scico.2022.102907).
Abstract
Stepwise development supported by the Event-B formalism has been used in the domain of system design and verification. This refinement approach guarantees that safety properties are preserved with Event-B proof obligations, while additional reasoning and fairness assumptions are required to prove the transformation of liveness properties in Event-B models. This paper presents a new proof-based approach that integrates Linear Temporal Logic (LTL) and Event-B for reasoning about the refinement of liveness properties. We first developed an extended version of LTL that could be used in Event-B models with three basic atomic propositions: state-related propositions, event-related propositions, and enabledness of events. Then we employed this extended LTL to express four important temporal properties with Event-B proof obligations and fairness assumptions. Besides the typical Event-B proof obligations, we specified conditions such as relative deadlock freeness, conditional convergence, and fairness assumptions to allow temporal properties to be transformed during refinement steps. The generic fairness-based refinement strategies were developed to replace or strengthen the fairness assumptions in the refinement steps of Event-B models. A reliable retransmission example is used to illustrate the approach.
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More information
Accepted/In Press date: 13 November 2022
e-pub ahead of print date: 17 November 2022
Published date: January 2023
Additional Information:
Funding Information:
Our sincere thanks go to anonymous reviewers who provided helpful suggestions to improve the quality of the paper. This work is supported in part by National Natural Science Foundation of China (No. 62202067 ), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (No. 22KJB520012 ).
Publisher Copyright:
© 2022 Elsevier B.V.
Keywords:
Event-B, Fairness assumptions, Linear temporal logic, Refinement
Identifiers
Local EPrints ID: 474841
URI: http://eprints.soton.ac.uk/id/eprint/474841
ISSN: 0167-6423
PURE UUID: f0a5b8ae-970f-418e-807c-edc2c71377c8
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Date deposited: 03 Mar 2023 17:45
Last modified: 17 Mar 2024 03:39
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