Abstract. Many multithreaded programs employ concurrent data types to safely share data among threads. However, highly-concurrent algorithms for even seemingly simple data types are difficult to implement correctly, especially when considering the relaxed memory ordering models commonly employed by today's multiprocessors. The formal verification of such implementations is challenging as well because the high degree of concurrency leads to a large number of possible executions. In this case study, we develop a SAT-based bounded verification method and apply it to a representative example, a well-known twolock concurrent queue algorithm. We first formulate a correctness criterion that specifically targets failures caused by concurrency; it demands that all concurrent executions be observationally equivalent to some serial execution. Next, we define a relaxed memory model that conservatively approximates several common shared-memory multiprocessors. Using commit point specifications, a suite of finite symbolic tests, a prototype encoder, and a standard SAT solver, we successfully identify two failures of a naive implementation that can be observed only under relaxed memory models. We eliminate these failures by inserting appropriate memory ordering fences into the code. The experiments confirm that our approach provides a valuable aid for desigining and implementing concurrent data types.

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This paper presents a randomized scheduler for finding concurrency bugs. Like current stress-testing methods, it repeatedly runs a given test program with supplied inputs. However, it improves on stress-testing by finding buggy schedules more effectively and by quantifying the probability of missing concurrency bugs. Key to its design is the characterization of the depth of a concurrency bug as the minimum number of scheduling constraints required to find it. In a single run of a program with n threads and k steps, our scheduler detects a concurrency bug of depth d with probability at least 1/ nk d-1 . We hypothesize that in practice, many concurrency bugs (including well-known types such as ordering errors, atomicity violations, and deadlocks) have small bug-depths, and we confirm the efficiency of our schedule randomization by detecting previously unknown and known concurrency bugs in several production-scale concurrent programs.

Program verification for relaxed memory models is hard. The high degree of nondeterminism in such models challenges standard verification techniques. This paper proposes a new verification technique for the most common relaxation, store buffers. Crucial to this technique is the observation that all programmers, including those who use low-lock techniques for performance, expect their programs to be sequentially consistent. We first present a monitor algorithm that can detect the presence of program executions that are not sequentially consistent due to store buffers while only exploring sequentially consistent executions. Then, we combine this monitor with a stateless model checker that verifies that every sequentially consistent execution is correct. We have implemented this algorithm in a prototype tool called Sober and present experiments that demonstrate the precision and scalability of our method. We find relaxed memory model bugs in several programs, including two previously unknown bugs in a production-level concurrency library that would have been difficult to find by other means.

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