On the Importance of Registers for Computability

All consensus hierarchies in the literature assume that we have, in addition to copies of a given object, an unbounded number of registers. But why do we really need these registers? This paper considers what would happen if one attempts to solve consensus using various objects but without any registers. We show that under a reasonable assumption, objects like queues and stacks cannot emulate the missing registers. We also show that, perhaps surprisingly, initialization, shown to have no computational consequences when registers are readily available, is crucial in determining the synchronization power of objects when no registers are allowed. Finally, we show that without registers, the number of available objects affects the level of consensus that can be solved. Our work thus raises the question of whether consensus hierarchies which assume an unbounded number of registers truly capture synchronization power, and begins a line of research aimed at better understanding the interaction between read-write memory and the powerful synchronization operations available on modern architectures.Comment: 12 pages, 0 figure

On the nature of progress

15th International Conference, OPODIS 2011, Toulouse, France, December 13-16, 2011. ProceedingsWe identify a simple relationship that unifies seemingly unrelated progress conditions ranging from the deadlock-free and starvation-free properties common to lock-based systems, to non-blocking conditions such as obstruction-freedom, lock-freedom, and wait-freedom. Properties can be classified along two dimensions based on the demands they make on the operating system scheduler. A gap in the classification reveals a new non-blocking progress condition, weaker than obstruction-freedom, which we call clash-freedom. The classification provides an intuitively-appealing explanation why programmers continue to devise data structures that mix both blocking and non-blocking progress conditions. It also explains why the wait-free property is a natural basis for the consensus hierarchy: a theory of shared-memory computation requires an independent progress condition, not one that makes demands of the operating system scheduler

Tuning the Level of Concurrency in Software Transactional Memory: An Overview of Recent Analytical, Machine Learning and Mixed Approaches

Synchronization transparency offered by Software Transactional Memory (STM) must not come at the expense of run-time efficiency, thus demanding from the STM-designer the inclusion of mechanisms properly oriented to performance and other quality indexes. Particularly, one core issue to cope with in STM is related to exploiting parallelism while also avoiding thrashing phenomena due to excessive transaction rollbacks, caused by excessively high levels of contention on logical resources, namely concurrently accessed data portions. A means to address run-time efficiency consists in dynamically determining the best-suited level of concurrency (number of threads) to be employed for running the application (or specific application phases) on top of the STM layer. For too low levels of concurrency, parallelism can be hampered. Conversely, over-dimensioning the concurrency level may give rise to the aforementioned thrashing phenomena caused by excessive data contention—an aspect which has reflections also on the side of reduced energy-efficiency. In this chapter we overview a set of recent techniques aimed at building “application-specific” performance models that can be exploited to dynamically tune the level of concurrency to the best-suited value. Although they share some base concepts while modeling the system performance vs the degree of concurrency, these techniques rely on disparate methods, such as machine learning or analytic methods (or combinations of the two), and achieve different tradeoffs in terms of the relation between the precision of the performance model and the latency for model instantiation. Implications of the different tradeoffs in real-life scenarios are also discussed

An Epistemic Perspective on Consistency of Concurrent Computations

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such consistency properties that is based on a standard logic of knowledge. Our formalization provides a declarative perspective on what is imposed by consistency requirements and provides some interesting unifying insight on differently looking properties

Bounded Model Checking of Concurrent Data Types on Relaxed Memory Models: A Case Study

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 two-lock 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

On the Computational Power of Shared Objects

Abstract. We propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. We use the strongest progress condition to associate with each object a number call the power number of that object. Objects with higher power numbers are considered stronger. Then, we define the power hierarchy which is an infinite hi-erarchy of objects such that the objects at level i of the hierarchy are exactly those objects with power number i. Comparing our classification with the traditional one which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Our equivalence and extended universality results, provide a deeper understanding of the nature of the relative computational power of shared objects

Faster linearizability checking via PP-compositionality

Linearizability is a well-established consistency and correctness criterion for concurrent data types. An important feature of linearizability is Herlihy and Wing's locality principle, which says that a concurrent system is linearizable if and only if all of its constituent parts (so-called objects) are linearizable. This paper presents $P$-compositionality, which generalizes the idea behind the locality principle to operations on the same concurrent data type. We implement $P$-compositionality in a novel linearizability checker. Our experiments with over nine implementations of concurrent sets, including Intel's TBB library, show that our linearizability checker is one order of magnitude faster and/or more space efficient than the state-of-the-art algorithm.Comment: 15 pages, 2 figure

On Correctness of Data Structures under Reads-Write Concurrency

Abstract. We study the correctness of shared data structures under reads-write concurrency. A popular approach to ensuring correctness of read-only operations in the presence of concurrent update, is read-set validation, which checks that all read variables have not changed since they were first read. In practice, this approach is often too conserva-tive, which adversely affects performance. In this paper, we introduce a new framework for reasoning about correctness of data structures under reads-write concurrency, which replaces validation of the entire read-set with more general criteria. Namely, instead of verifying that all read conditions over the shared variables, which we call base conditions. We show that reading values that satisfy some base condition at every point in time implies correctness of read-only operations executing in parallel with updates. Somewhat surprisingly, the resulting correctness guarantee is not equivalent to linearizability, and is instead captured through two new conditions: validity and regularity. Roughly speaking, the former re-quires that a read-only operation never reaches a state unreachable in a sequential execution; the latter generalizes Lamport’s notion of regular-ity for arbitrary data structures, and is weaker than linearizability. We further extend our framework to capture also linearizability. We illus-trate how our framework can be applied for reasoning about correctness of a variety of implementations of data structures such as linked lists.

What Can Be Implemented Anonymously?

Abstract. The vast majority of papers on distributed computing assume that processes are assigned unique identifiers before computation begins. But is this assumption necessary? What if processes do not have unique identifiers or do not wish to divulge them for reasons of privacy? We consider asynchronous shared-memory systems that are anonymous. The shared memory contains only the most common type of shared objects, read/write registers. We investigate, for the first time, what can be implemented deterministically in this model when processes can fail. We give anonymous algorithms for some fundamental problems: timestamping, snapshots and consensus. Our solutions to the first two are wait-free and the third is obstruction-free. We also show that a shared object has an obstruction-free implementation if and only if it satisfies a simple property called idempotence. To prove the sufficiency of this condition, we give a universal construction that implements any idempotent object