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Distributed protocols have long been formulated in terms of their safety and liveness properties. Much recent work has focused on automatically verifying the safety properties of distributed protocols, but doing so for liveness properties has remained a challenging, unsolved problem. We present LVR, the first framework that can mostly automatically verify liveness properties for distributed protocols. Our key insight is that most liveness properties for distributed protocols can be reduced to a set of safety properties with the help of ranking functions. Such ranking functions for practical distributed protocols have certain properties that make them straightforward to synthesize, contrary to conventional wisdom. We prove that verifying a liveness property can then be reduced to a simpler problem of verifying a set of safety properties, namely that the ranking function is strictly decreasing and nonnegative for any protocol state transition, and there is no deadlock. LVR automatically synthesizes ranking functions by formulating a parameterized function of integer protocol variables, statically analyzing the lower and upper bounds of the variables as well as how much they can change on each state transition, then feeding the constraints to an SMT solver to determine the coefficients of the ranking function. It then uses an off-the-shelf verification tool to find inductive invariants to verify safety properties for both ranking functions and deadlock freedom. We show that LVR can mostly automatically verify the liveness properties of several distributed protocols, including various versions of Paxos, with limited user guidance. 

Concurrent systems software is widely-used, complex, and error-prone, posing a significant security risk. We introduce VRM, a new framework that makes it possible for the first time to verify concurrent systems software, such as operating systems and hypervisors, on Arm relaxed memory hardware. VRM defines a set of synchronization and memory access conditions such that a program that satisfies these conditions can be mostly verified on a sequentially consistent hardware model and the proofs will automatically hold on relaxed memory hardware. VRM can be used to verify concurrent kernel code that is not data race free, including code responsible for managing shared page tables in the presence of relaxed MMU hardware. Using VRM, we verify the security guarantees of a retrofitted implementation of the Linux KVM hypervisor on Arm. For multiple versions of KVM, we prove KVM's security properties on a sequentially consistent model, then prove that KVM satisfies VRM's required program conditions such that its security proofs hold on Arm relaxed memory hardware. Our experimental results show that the retrofit and VRM conditions do not adversely affect the scalability of verified KVM, as it performs similar to unmodified KVM when concurrently running many multiprocessor virtual machines with real application workloads on Arm multiprocessor server hardware. Our work is the first machine-checked proof for concurrent systems software on Arm relaxed memory hardware.