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An important property of concurrent objects is whether they support progress -a special case of liveness-guarantees, which ensure the termination of individual method calls under system fairness assumptions. Liveness properties have been proposed for concurrent objects. Typical liveness properties includelock-freedom,wait-freedom,deadlock-freedom,starvation-freedom and obstruction-freedom. It is known that the five liveness properties above are decidable on the Sequential Consistency (SC) memory model for a bounded number of processes. However, the problem of decidability of liveness for finite state concurrent programs running on relaxed memory models remains open. In this paper we address this problem for the Total Store Order (TSO) memory model,as found in the x86 architecture. We prove that lock-freedom, wait-freedom,deadlock-freedom and starvation-freedom are undecidable on TSO for a bounded number of processes, while obstruction-freedom is decidable.

We study a proof methodology for verifying the safety of data invariants of highly-available distributed applications that replicate state. The proof is (1) modular: one can reason about each individual operation separately, and (2) sequential: one can reason about a distributed application as if it were sequential. We automate the methodology and illustrate the use of the tool with a representative example., Comment: Workshop on Principles and Practice of Consistency for Distributed Data (PaPoC), Mar 2019, Dresden, Germany. https://novasys.di.fct.unl.pt/conferences/papoc19/