Abstract
In an actor system, detecting global idleness is trivial if the global state can be inspected synchronously. A distributed implementation, especially with asynchronous messages, poses more problems. This paper discusses detecting idleness in actor systems with various characteristics, among them topology and message passing semantics. We present a TLA+ specification of a simple termination detection algorithm, add necessary conditions missing in the original description, and establish a correctness invariant to model-check the specification against. We further show via model-checking that the algorithm only works with synchronous messages but is robust against message reordering. We then model and discuss a simplified version of the idleness detection implementation in the Erlang backend of the ABS modeling language.
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Acknowledgements
The development of ABS was supported by the EU projects HATS and Envisage. Reiner Hähnle participated in Envisage and coordinated HATS; his influence on the development and developer of ABS is gratefully acknowledged.
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Appendices
A Dijkstra’s Algorithm
B Asynchronous Message Sending in the Dijkstra Algorithm Model
Add the inbox variable and replace the rule \( sendMsg(i, j) \) of Appendix A with the two rules sendMsg, becomeActive as follows:
C Specification of the Erlang Backend Behavior
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Schlatte, R. (2022). A Note on Idleness Detection of Actor Systems. In: Ahrendt, W., Beckert, B., Bubel, R., Johnsen, E.B. (eds) The Logic of Software. A Tasting Menu of Formal Methods. Lecture Notes in Computer Science, vol 13360. Springer, Cham. https://doi.org/10.1007/978-3-031-08166-8_21
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DOI: https://doi.org/10.1007/978-3-031-08166-8_21
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