Abstract

Dependable properties such as self-stabilization are crucial requirements in sensor networks. One way to achieve these properties is to utilize the vast literature on distributed systems where such self-stabilizing algorithms have been designed. Since these existing algorithms are designed in read/write model (or variations thereof), they cannot be directly applied in sensor networks. For this reason, we consider a new atomicity model, write all with collision (WAC), that captures the computations of sensor networks and focus on transformations from read/write model to WAC model and vice versa. We show that the transformation from WAC model to read/write model is stabilization preserving, and the transformation from read/write model to WAC model is stabilization preserving for timed systems. In the transformation from read/write model to WAC model, if the system is untimed (asynchronous) and processes are deterministic then under reasonable assumptions, we show that (1) the resulting program in WAC model can allow at most one process to execute, and (2) the resulting program in WAC model cannot be stabilizing.

Keywords: Dependability; Self-stabilization; Write-all-with-collision model; Read/write model; Model conversions

Article Outline

1. Introduction

1.1. Existing models and semantics of distributed programs

1.2. Contributions of the paper

1.3. Organization of the paper

2. Preliminaries

2.1. Read/write model

2.2. WAC model

2.3. Preserving stabilization

2.4. System assumptions

3. Read/write model to WAC model in untimed systems

3.1. Optimality issues

3.2. Impossibility of preserving stabilization in untimed systems

4. Read/write model to WAC model in timed systems

4.1. Transformation algorithm for a grid topology

4.2. Transformation algorithm for an arbitrary topology

4.3. Preserving stabilization in timed systems

5. Illustration: transformation of a routing program

5.1. LGRP program in read/write model

5.2. LGRP program in WAC model

6. WAC model to read/write model

6.1. Preserving stabilization

7. Discussion

7.1. In the transformation shown in Section 6, the value of counter is unbounded. Can it be bounded?

8. Conclusion and future work

Acknowledgements

Appendix A. Optimality issues in untimed systems

Appendix B. Redundant writes in untimed systems

B.1. Concurrent executions

References

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