# Rely-Guarantee Termination and Cost Analyses of Loops with Concurrent Interleavings

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## Abstract

By following a *rely-guarantee* style of reasoning, we present novel termination and cost analyses for concurrent programs that, in order to prove termination or infer the cost of a considered loop: (1) infer the termination/cost of each loop as if it were a sequential one, imposing assertions on how shared-data is modified concurrently; and then (2) prove that these assertions cannot be violated infinitely many times and, for cost analysis, infer how many times they are violated. At the core of the analysis, we use a *may-happen-in-parallel* analysis to restrict the set of program points whose execution can interleave. Interestingly, the same kind of reasoning can be applied to prove termination and infer *upper bounds* on the number of iterations of loops with concurrent interleavings. To the best of our knowledge, this is the first method to automatically bound the cost of such kind of loops. We have implemented our analysis for an *actor-based* language, and showed its accuracy and efficiency by applying it on several typical applications for concurrent programs and on an industrial case study.

## Keywords

Static analysis Actor model Concurrency Rely-guarantee Termination analysis Cost analysis May-happen-in-parallel analysis## Notes

### Acknowledgements

Funding was provided by Seventh Framework Programme (EU) (Grant no. FP7-ICT-610582), Ministerio de Economía y Competitividad (ES) (Grant nos. TIN2012-38137, TIN2015-69175-C4-2-R), and Comunidad de Madrid (ES) (Grant no. S2013/ICE-3006).

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