Weak-memory models are standard formal specifications of concurrency across hardware, programming languages, and distributed systems. A fundamental computational problem is consistency testing: is the observed execution of a concurrent program in alignment with the specification of the underlying system? The problem has been studied extensively across Sequential Consistency (SC) and weak memory, and proven to be NP-complete when some aspect of the input (e.g., number of threads/memory locations) is unbounded. This unboundedness has left a natural question open: are there efficient parameterized algorithms for testing? The main contribution of this paper is a deep hardness result for consistency testing under many popular weak-memory models: the problem remains NP-complete even in its bounded setting, where candidate executions contain a bounded number of threads, memory locations, and values. This hardness spreads across several Release-Acquire variants of C11, a popular variant of its Relaxed fragment, popular Causal Consistency models, and the POWER architecture. To our knowledge, this is the first result that fully exposes the hardness of weak-memory testing and proves that the problem admits no parameterization under standard input parameters. It also yields a computational separation of these models from SC, x86-TSO, PSO, and Relaxed, for which bounded consistency testing is either known (for SC), or shown here (for the rest), to be in polynomial time.

Over the years, several memory models have been proposed to capture the subtle concurrency semantics of C/C++. One of the most fundamental problems associated with a memory model M is consistency checking: given an execution X, is X consistent with M? This problem lies at the heart of numerous applications, including specification testing and litmus tests, stateless model checking, and dynamic analyses. As such, it has been explored extensively and its complexity is well-understood for traditional models like SC and TSO. However, less is known for the numerous model variants of C/C++, for which the problem becomes challenging due to the intricacies of their concurrency primitives. In this work we study the problem of consistency checking for popular variants of the C11 memory model, in particular, the RC20 model, its release-Acquire (RA) fragment, the strong and weak variants of RA (SRA and WRA), as well as the Relaxed fragment of RC20. Motivated by applications in testing and model checking, we focus on reads-from consistency checking. The input is an execution X specifying a set of events, their program order and their reads-from relation, and the task is to decide the existence of a modification order on the writes of X that makes X consistent in a memory model. We draw a rich complexity landscape for this problem; our results include (i) nearly-linear-Time algorithms for certain variants, which improve over prior results, (ii) fine-grained optimality results, as well as (iii) matching upper and lower bounds (NP-hardness) for other variants. To our knowledge, this is the first work to characterize the complexity of consistency checking for C11 memory models. We have implemented our algorithms inside the TruSt model checker and the C11Tester testing tool. Experiments on standard benchmarks show that our new algorithms improve consistency checking, often by a significant margin.