State space abstraction for parameterized self-stabilizing embedded systems

Authors:
Nikolaos Liveris;Hai Zhou;Robert P. Dick;Prithviraj Banerjee
Affiliations:
Northwestern University, Evanston, IL, USA;Northwestern University, Evanston, IL, USA;Northwestern University, Evanston, IL, USA;HP Labs, Palo Alto, CA, USA
Venue:
EMSOFT '08 Proceedings of the 8th ACM international conference on Embedded software
Year:
2008

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Abstract

Self-stabilizing systems are systems that automatically recover from any transient fault. Proving the correctness of a parameterized self-stabilizing system, i.e., a system composed of an arbitrary number of processes, is a challenging task. For the verification of parameterized systems the method of control abstraction has been developed. However, control abstraction can only be applied to systems in which each process has a fixed number of observable variables. In this article, we propose a technique to abstract a parameterized self-stabilizing system, whose processes have a parameterized number of observable variables, to a system with fixed number of observable variables. This enables the use of control abstraction for verification. The proposed technique targets low-atomicity, shared-memory, asynchronous systems. We establish the completeness of the method under reasonable conditions and demonstrate its effectiveness by applying it on a number of self-stabilizing distributed systems.