Read-Copy-Update (RCU) is a critical synchronization mechanism for concurrent data structures, enabling efficient deferred memory reclamation. However, implementing and using RCU correctly is challenging due to its inherent concurrency complexities. While previous work verified RCU, they either relied on unrealistic assumptions of sequentially consistent (SC) memory model or lacked three key features of general-purpose RCU libraries: modular specification, switchable critical sections, and concurrent writer support. We present the first formal verification of a general-purpose RCU in realistic relaxed memory consistency (RMC), addressing the challenges posed by these features. To achieve modular specification that encompasses relaxed behaviors, we extend existing SC specifications to account for explicit synchronization. To support switchable critical sections, which require read-after-write (RAW) synchronization, we introduce a reasoning principle for RAW-synchronizing SC fences . Using this principle, we also present the first formal verification of Peterson's mutex in RMC. To support concurrent writers performing partially ordered writes, we avoid assuming a total order of links and instead formulate invariants based on per-node incoming link histories. Our proofs are mechanized in the iRC11 relaxed memory separation logic, built upon Iris, in Rocq.

We report the first formal verification of a lock-free list, skiplist, and a skiplist-based priority queue against a strong specification in relaxed memory consistency (RMC). RMC allows relaxed behaviors in which memory accesses may be reordered with other operations, posing two significant challenges for the verification of lock-free traversals. (1) Specification challenge : formulating a specification that is flexible enough to capture relaxed behaviors, yet simple enough to be easily understood and used. We address this challenge by proposing the per-key linearizable history specification that enforces a total order of operations for each key that respects causality, rather than a total order of all operations. (2) Verification challenge : devising verification techniques for reasoning about the reachability of edges for traversing threads, which can read stale edges due to relaxed behaviors. We address this challenge by introducing the shadowed-by relation that formalizes the notion of outdated edges. This relation enables us to establish a total order of edges and thus their associated operations for each key, required to satisfy the strong specification. All our proofs are mechanized on the iRC11 relaxed memory separation logic, built on the Iris framework in Rocq.

Reclamation schemes for concurrent data structures tackle the challenge of synchronizing memory accesses and reclamation. Early schemes faced a tradeoff between robustness and efficiency : hazard pointers (HP) bounds the number of unreclaimed nodes, but it is inefficient due to per-node protection; and RCU sacrifices robustness for efficiency as a single thread may block the entire reclamation. Recent schemes attempt to break the tradeoff by sending signals to blocking threads to abort their operations. However, they are (1)inefficient due to starvation in long-running operations and frequent signals, and (2)inapplicable to a wide class of data structures.

Memory management for optimistic concurrency in unmanaged programming languages is challenging. Safe memory reclamation (SMR) algorithms help address this, but they are difficult to use correctly. Automatic reference counting provides a simpler interface, but it has been less efficient than SMR algorithms. Recently, there has been a push to apply the optimizations used in garbage collectors for managed languages to elide reference count updates from local references. Notably, Fast Reference Counter, OrcGC, and Concurrent Deferred Reference Counting use SMR algorithms to protect local references by deferring decrements or reclamation. While they show a significant performance improvement, their use of deferral may result in growing memory usage due to slow reclamation of linked structures, and suboptimal performance in update-heavy workloads. We present Concurrent Immediate Reference Counting (CIRC), a new combination of SMR algorithms with reference counting. CIRC employs deferral like other modern methods, but it avoids their problems with novel algorithms for (1) immediately reclaiming linked structures recursively by tracking the reachability of each object, and (2) applying decrements immediately and deferring only the reclamation. Our experiments show that CIRC’s memory usage does not grow over time and is only slightly higher than the underlying SMR. Moreover, CIRC further narrows the performance gap between the underlying SMR, positioning it as a promising solution to safe automatic memory management for highly concurrent data structures in unmanaged languages.

Linearizability is the de facto standard for correctness of concurrent objects–it essentially says that all the object’s operations behave as if they were atomic. There have been a number of recent advances in developing increasingly strong linearizability specifications for relaxed memory consistency (RMC), but scalable proof methods for these specifications do not exist due to the challenges arising from out-of-order executions (requiring event reordering) and selected synchronization (requiring tracking of view transfers). We propose a proof recipe for the linearizable history specifications by Dang et al . in the Iris-based iRC11 concurrent separation logic in Coq. Key to our proof recipe is the notion of object modification order (OMO) , which generalizes the modification order of the C11 memory model to an object-local setting. Using OMO we minimize the conditions that need to be proved for event reordering. To enable proof reuse for concurrent libraries that are built on top of others, OMO provides the novel notion of a commit-with relation that connects the linearization points of the lower and upper libraries. Using our recipe, we verify the linearizability of the Michael–Scott queue, the elimination stack, and Folly’s MPMC queue in RMC for the first time; and verify stronger specifications of a spinlock and atomic reference counting in RMC than prior work.

Hazard pointers is a popular semi-manual memory reclamation scheme for concurrent data structures, where each accessing thread announces protection of each object to access and validates that the pointer is not already freed. Validation is typically done by over-approximating unreachability: if an object seems to be unreachable from the root of the data structure, the protecting thread decides not to access the object as it might have been freed. However, many efficient data structures are incompatible with validation by over-approximation as their optimistic traversal strategy intentionally ignores the warning of unreachability to achieve better performance.

Formal verification is an effective method to address the challenge of designing correct and efficient concurrent data structures. But verification efforts often ignore memory reclamation , which involves nontrivial synchronization between concurrent accesses and reclamation. When incorrectly implemented, it may lead to critical safety errors such as use-after-free and the ABA problem. Semi-automatic safe memory reclamation schemes such as hazard pointers and RCU encapsulate the complexity of manual memory management in modular interfaces. However, this modularity has not been carried over to formal verification. We propose modular specifications of hazard pointers and RCU, and formally verify realistic implementations of them in concurrent separation logic. Specifically, we design abstract predicates for hazard pointers that capture the meaning of validating the protection of nodes, and those for RCU that support optimistic traversal to possibly retired nodes. We demonstrate that the specifications indeed facilitate modular verification in three criteria: compositional verification, general applicability, and easy integration. In doing so, we present the first formal verification of Harris’s list, the Harris-Michael list, the Chase-Lev deque, and RDCSS with reclamation. We report the Coq mechanization of all our results in the Iris separation logic framework.

Several functional correctness criteria have been proposed for relaxed-memory consistency libraries, but most lack support for modular client reasoning. Mével and Jourdan recently showed that logical atomicity can be used to give strong modular Hoare-style specifications for relaxed libraries, but only for a limited instance in the Multicore OCaml memory model. It has remained unclear if their approach scales to weaker implementations in weaker memory models.

All pointer-based nonblocking concurrent data structures should deal with the problem of safe memory reclamation: before reclaiming a memory block, a thread should ensure no other threads hold a local pointer to the block that may later be dereferenced. Various safe memory reclamation schemes have been proposed in the literature, but none of them satisfy the following desired properties at the same time: (i) robust: a non-cooperative thread does not prevent the other threads from reclaiming an unbounded number of blocks; (ii) fast: it does not incur significant time overhead; (iii) compact: it does not incur significant space overhead; (iv) self-contained: it neither relies on special hardware/OS supports nor intrusively affects execution environments; and (v) widely applicable: it supports many data structures.