Polynomial-Time Verification and Testing of Implementations of the Snapshot Data Structure

We analyze correctness of implementations of the snapshot data structure in terms of linearizability. We show that such implementations can be verified in polynomial time. Additionally, we identify a set of representative executions for testing and show that the correctness of each of these executions can be validated in linear time. These results present a significant speedup considering that verifying linearizability of implementations of concurrent data structures, in general, is EXPSPACE-complete in the number of program-states, and testing linearizability is NP-complete in the length of the tested execution. The crux of our approach is identifying a class of executions, which we call simple, such that a snapshot implementation is linearizable if and only if all of its simple executions are linearizable. We then divide all possible non-linearizable simple executions into three categories and construct a small automaton that recognizes each category. We describe two implementations (one for verification and one for testing) of an automata-based approach that we develop based on this result and an evaluation that demonstrates significant improvements over existing tools. For verification, we show that restricting a state-of-the-art tool to analyzing only simple executions saves resources and allows the analysis of more complex cases. Specifically, restricting attention to simple executions finds bugs in 27 instances, whereas, without this restriction, we were only able to find 14 of the 30 bugs in the instances we examined. We also show that our technique accelerates testing performance significantly. Specifically, our implementation solves the complete set of 900 problems we generated, whereas the state-of-the-art linearizability testing tool solves only 554 problems

Putting Strong Linearizability in Context: Preserving Hyperproperties in Programs That Use Concurrent Objects

It has been observed that linearizability, the prevalent consistency condition for implementing concurrent objects, does not preserve some probability distributions. A stronger condition, called strong linearizability has been proposed, but its study has been somewhat ad-hoc. This paper investigates strong linearizability by casting it in the context of observational refinement of objects. We present a strengthening of observational refinement, which generalizes strong linearizability, obtaining several important implications. When a concrete concurrent object refines another, more abstract object - often sequential - the correctness of a program employing the concrete object can be verified by considering its behaviors when using the more abstract object. This means that trace properties of a program using the concrete object can be proved by considering the program with the abstract object. This, however, does not hold for hyperproperties, including many security properties and probability distributions of events. We define strong observational refinement, a strengthening of refinement that preserves hyperproperties, and prove that it is equivalent to the existence of forward simulations. We show that strong observational refinement generalizes strong linearizability. This implies that strong linearizability is also equivalent to forward simulation, and shows that strongly linearizable implementations can be composed both horizontally (i.e., locality) and vertically (i.e., with instantiation). For situations where strongly linearizable implementations do not exist (or are less efficient), we argue that reasoning about hyperproperties of programs can be simplified by strong observational refinement of non-atomic abstract objects

Characterizing Implementations that Preserve Properties of Concurrent Randomized Algorithms

We show that correctness criteria of concurrent algorithms are mathematically equivalent to the existence of so-called simulations between implementations of the algorithms in a well-known framework (that of input/output automata) and simple canonical automata. This equivalence allows us to frame our proofs of correctness in a language much more amenable to machine-checking than conventional proofs. We give the first demonstration that when strongly linearizable implementations of randomized concurrent algorithms are utilized, then the distributions of a well-defined class of random variables are preserved under object substitution by non-concurrent implementations of the same algorithms. We also consider weaker conditions than strong linearizability under which implementations are still correct in the presence of randomization

The ERA Theorem for Safe Memory Reclamation

Safe memory reclamation (SMR) schemes for concurrent data structures offer trade-offs between three desirable properties: ease of integration, robustness, and applicability. In this paper we rigorously define SMR and these three properties, and we present the ERA theorem, asserting that any SMR scheme can only provide at most two of the three properties

Laws of order

Building correct and efficient concurrent algorithms is known to be a difficult problem of fundamental importance. To achieve efficiency, designers try to remove unnecessary and costly synchronization. However, not only is this manual trial-and-error process ad-hoc, time consuming and error-prone, but it often leaves designers pondering the question of: is it inherently impossible to eliminate certain synchronization, or is it that I was unable to eliminate it on this attempt and I should keep trying? In this paper we respond to this question. We prove that it is impossible to build concurrent implementations of classic and ubiquitous specifications such as sets, queues, stacks, mutual exclusion and read-modify-write operations, that completely eliminate the use of expensive synchronization. We prove that one cannot avoid the use of either: i) read-after-write (RAW), where a write to shared variable A is followed by a read to a different shared variable B without a write to B in between, or ii) atomic write-after-read (AWAR), where an atomic operation reads and then writes to shared locations. Unfortunately, enforcing RAW or AWAR is expensive on all current mainstream processors. To enforce RAW, memory ordering--also called fence or barrier--instructions must be used. To enforce AWAR, atomic instructions such as compare-and-swap are required. However, these instructions are typically substantially slower than regular instructions. Although algorithm designers frequently struggle to avoid RAW and AWAR, their attempts are often futile. Our result characterizes the cases where avoiding RAW and AWAR is impossible. On the flip side, our result can be used to guide designers towards new algorithms where RAW and AWAR can be eliminated

VBR: Version Based Reclamation

Safe lock-free memory reclamation is a difficult problem. Existing solutions follow three basic methods (or their combinations): epoch based reclamation, hazard pointers, and optimistic reclamation. Epoch-based methods are fast, but do not guarantee lock-freedom. Hazard pointer solutions are lock-free but typically do not provide high performance. Optimistic methods are lock-free and fast, but previous optimistic methods did not go all the way. While reads were executed optimistically, writes were protected by hazard pointers. In this work we present a new reclamation scheme called version based reclamation (VBR), which provides a full optimistic solution to lock-free memory reclamation, obtaining lock-freedom and high efficiency. Speculative execution is known as a fundamental tool for improving performance in various areas of computer science, and indeed evaluation with a lock-free linked-list, hash-table and skip-list shows that VBR outperforms state-of-the-art existing solutions