Abstract
Today, numerous elaborate algorithms for the effective synchronization of concurrent processes operating on shared memory exist. Of particular importance for the verification of such concurrent algorithms are thread-local proof techniques, which allow to reason about the sequential program of one process individually. While thread-local verification of safety properties has received a lot of attention in recent years, this is less so for liveness properties, in particular for liveness under the assumption of fairness.
In this paper, we propose a new thread-local proof technique for starvation freedom. Starvation freedom states that under a weakly fair schedule every process will eventually make progress. We contrast our new proof technique with existing global proof techniques based on ranking functions, and employ it exemplarily for the proof of starvation freedom of ticket locks, the standard locking algorithm of the Linux kernel.
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Notes
- 1.
The encoding in the theorem prover KIV does this explicitly.
- 2.
The notation in KIV proofs is \(pre \mathop {\rightarrow }\ [: \underline{x} \mid R,G,I, P] post\).
- 3.
For simplicity, we assume the algorithm is not recursive. However, the argument of getting stuck in a recursion is not really different.
- 4.
Both proofs are done for a slight extension of the theory we do not discuss in this paper. This extension establishes linearizability (simply due to mutual exclusion) for an arbitrary operation in the critical section by using slightly enhanced versions of \(R_p\), \(I_p\) and \(G_p\).
- 5.
With the exception of [13] discussed in the introduction.
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Schellhorn, G., Travkin, O., Wehrheim, H. (2016). Towards a Thread-Local Proof Technique for Starvation Freedom. In: Ábrahám, E., Huisman, M. (eds) Integrated Formal Methods. IFM 2016. Lecture Notes in Computer Science(), vol 9681. Springer, Cham. https://doi.org/10.1007/978-3-319-33693-0_13
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