The size of collections, maps, and data structures in general, constitutes a fundamental property. An implementation of the size method is required in most programming environments. Nevertheless, in a concurrent environment, integrating a linearizable concurrent size introduces a noticeable overhead on all operations of the data structure, even when the size method is not invoked during the execution. In this work we present a study of synchronization methods in an attempt to improve the performance of the data structure. In particular, we study a handshake technique that is commonly used with concurrent garbage collection, an optimistic technique, and a lock-based technique. Evaluation against the state-of-the-art size methodology demonstrates that the overhead can be significantly reduced by selecting the appropriate synchronization approach, but there is no one-size-fits-all method. Different scenarios call for different synchronization methods, as rigorously shown in this study. Nevertheless, our findings align with general trends in concurrent computing. In scenarios characterized by low contention, optimistic and lock-based approaches work best, whereas under high contention, the most effective solutions are the handshake approach and the wait-free approach.

Compaction algorithms alleviate fragmentation by relocating heap objects to compacted areas. A full heap compaction eliminates fragmentation by compacting all objects into the lower addresses of the heap. Following a marking phase that marks all reachable (live) objects, the compactor needs to copy all marked objects to the beginning of the address space and fix all pointers to reference the new object locations. Initially, this process required three heap passes (beyond the marking phase). However, modern algorithms, culminating in the Compressor, have reduced this cost to a single heap pass plus a single pass over an auxiliary table, that is smaller than (yet proportional to) the size of the heap. In this paper, we introduce the One Pass (OP) Compactor: a novel combination of existing compactors that reduces the complexity of compaction to a single heap pass. This represents arguably the best possible complexity for a compaction algorithm. Additionally, we extend the OP compactor with a parallel version, enabling scalability on a multicore platform. This paper is classified as an intellectual abstract because it introduces the new algorithm but does not provide an accompanying implementation and evaluation.

Recent non-volatile main memory technology gave rise to an abundance of research on building persistent data structures, whose content can be recovered after a system crash. While there has been significant progress in making durable data structures efficient, shortening the length of the recovery phase after a crash has not received much attention. In this paper we present the RELAX general transformation. RELAX generates lock-free durable data structures that provide the best of both worlds: almost zero recovery time and high performance.

Concurrent data structures serve as fundamental building blocks for concurrent computing. Many concurrent counterparts have been designed for basic sequential algorithms; however, one notable omission is a concurrent tree that supports aggregate queries. Aggregate queries essentially compile succinct information about a range of data items. Such queries play an essential role in various applications and are commonly taught in undergraduate data structures courses. In this paper, we formalize a type of aggregate queries that can be efficiently supported by concurrent trees and present a design for implementing these queries on concurrent lock-based trees. We present two algorithms implementing this design, where one optimizes for tree update time, while the other optimizes for aggregate query time.

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.

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 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.

Multi-Version Concurrency Control (MVCC) is a common mechanism for achieving linearizable range queries in database systems and concurrent data-structures. The core idea is to keep previous versions of nodes to serve range queries, while still providing atomic reads and updates. Existing concurrent data-structure implementations, that support linearizable range queries, are either slow, use locks, or rely on blocking reclamation schemes. We present EEMARQ, the first scheme that uses MVCC with lock-free memory reclamation to obtain a fully lock-free data-structure supporting linearizable inserts, deletes, contains, and range queries. Evaluation shows that EEMARQ outperforms existing solutions across most workloads, with lower space overhead and while providing full lock freedom.

Non-volatile random access memory (NVRAM) offers byte-addressable persistence at speeds comparable to DRAM. However, with caches remaining volatile, automatic cache evictions can reorder updates to memory, potentially leaving persistent memory in an inconsistent state upon a system crash. Flush and fence instructions can be used to force ordering among updates, but are expensive. This has motivated significant work studying how to write correct and efficient persistent programs for NVRAM.

The size of a data structure (i.e., the number of elements in it) is a widely used property of a data set. However, for concurrent programs, obtaining a correct size efficiently is non-trivial. In fact, the literature does not offer a mechanism to obtain a correct (linearizable) size of a concurrent data set without resorting to inefficient solutions, such as taking a full snapshot of the data structure to count the elements, or acquiring one global lock in all update and size operations. This paper presents a methodology for adding a concurrent linearizable size operation to sets and dictionaries with a relatively low performance overhead. Theoretically, the proposed size operation is wait-free with asymptotic complexity linear in the number of threads (independently of data-structure size). Practically, we evaluated the performance overhead by adding size to various concurrent data structures in Java−a skip list, a hash table and a tree. The proposed linearizable size operation executes faster by orders of magnitude compared to the existing option of taking a snapshot, while incurring a throughput loss of 1%−20% on the original data structure’s operations.

With the recent launch of the Intel Optane memory platform, non-volatile main memory in the form of fast, dense, byte-addressable non-volatile memory has now become available. Nevertheless, designing crash-resilient algorithms and data structures is complex and error-prone as caches and machine registers are still volatile and the data residing in memory after a crash might not reflect a consistent view of the program state. This complex setting has often led to durable data structures being inefficient or incorrect, especially in the concurrent setting.

Linearizability is the de facto consistency condition for concurrent objects, widely used in theory and practice. Loosely speaking, linearizability classifies concurrent executions as correct if operations on shared objects appear to take effect instantaneously during the operation execution time. This paper calls attention to a somewhat-neglected aspect of linearizability: restrictions on how pending invocations are handled, an issue that has become increasingly important for software running on systems with non-volatile main memory. Interestingly, the original published definition of linearizability includes a typo (a symbol is missing a prime) that concerns exactly this issue. In this paper we point out the typo and provide an amendment to make the definition complete. We believe that pointing this typo out rigorously and proposing a fix is important and timely.

We consider durable data structures for non-volatile main memory, such as the new Intel Optane memory architecture. Substantial recent work has concentrated on making concurrent data structures durable with low overhead, by adding a minimal number of blocking persist operations (i.e., flushes and fences). In this work we show that focusing on minimizing the number of persist instructions is important, but not enough. We show that access to flushed content is of high cost due to cache invalidation in current architectures. Given this finding, we present a design of the queue data structure that properly takes care of minimizing blocking persist operations as well as minimizing access to flushed content. The proposed design outperforms state-of-the-art durable queues.

Safe lock-free memory reclamation is a difficult problem. Existing solutions follow three basic methods: 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.

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.

The recent availability of fast, dense, byte-addressable non-volatile memory has led to increasing interest in the problem of designing durable data structures that can recover from system crashes. However, designing durable concurrent data structures that are correct and efficient has proven to be very difficult, leading to many inefficient or incorrect algorithms. In this paper, we present a general transformation that takes a lock-free data structure from a general class called traversal data structure (that we formally define) and automatically transforms it into an implementation of the data structure for the NVRAM setting that is provably durably linearizable and highly efficient. The transformation hinges on the observation that many data structure operations begin with a traversal phase that does not need to be persisted, and thus we only begin persisting when the traversal reaches its destination. We demonstrate the transformation's efficiency through extensive measurements on a system with Intel's recently released Optane DC persistent memory, showing that it can outperform competitors on many workloads.

Hardware and software faults increasingly surface in today's computing environment and vast theoretical and practical research efforts are being devoted to overcoming the effects of malfunctionality in the computing process. Most research to date, however, has focused on how to discover and handle faulty data. We initiate a formal study of faulty functionality in a modern multicore shared-memory environment. We introduce a model of functional faults, and study avenues that allow tolerating functional faults while maintaining the correctness of the entire computation. We demonstrate the generality of this model by constructing a robust consensus protocol from functionally-faulty compare-and-swap objects. Additionally, We formally prove (tight) impossibility result for the same constructions.

Hardware and software faults increasingly surface in today's computing environment and vast theoretical and practical research efforts are devoted to ameliorate the effects of malfunctionality in the computing process. Most research to date, however, has focused on how to discover and handle faulty data. In this paper we formalize and study faulty functionality in a modern multicore shared-memory environment. Functional faults have been previously studied in the architecture community. However, they have never been formally defined and lower/upper bounds were not previously proven. We present a model of functional faults, and study avenues that allow tolerating functional faults while maintaining the correctness of the entire computation. We exemplify this model by constructing a robust consensus protocol from functionally-faulty compare-and-swap objects. We then show a (tight) impossibility result for the same construction, when the number of faults exceeds a certain threshold. Interestingly, for some fault types, more functional faults can be tolerated than the analogue data faults, beating an impossibility result for data faults and demonstrating the difference between the two models.

Concurrent data structures are widely used in modern multicore architectures, providing atomicity (linearizability) for each concurrent operation. However, it is often desirable to execute several operations on multiple data structures atomically. We present a design of a transactional framework supporting linearizable transactions of multiple operations on multiple data structures in a lock-free manner. Our design uses a helping mechanism to obtain lock-freedom, and an advanced lock-free contention management mechanism to mitigate the effects of aborting transactions. When cyclic helping conflicts are detected, the contention manager reorders the conflicting transactions execution allowing all transactions to complete with minimal delay. To exemplify this framework we implement a transactional set using a skip-list, a transactional queue, and a transactional register. We present an evaluation of the system showing that we outperform general software transactional memory, and are competitive with lock-based transactional data structures.

Non-volatile memory is expected to co-exist or replace DRAM in upcoming architectures. Durable concurrent data structures for non-volatile memories are essential building blocks for constructing adequate software for use with these architectures. In this paper, we propose a new approach for durable concurrent sets and use this approach to build the most efficient durable hash tables available today. Evaluation shows a performance improvement factor of up to 3.3x over existing technology.

Concurrent data structures typically index data using a single primary key and provide fast atomic access to data associated with a given key value. However, it is often required to atomically access information via multiple primary and secondary keys, and even through additional properties that do not naturally represent keys for the given data. We present lock-free and lock-based algorithms of a table with multiple indexing, supporting linearizable inserts, deletes, and retrieve operations. We have implemented Java versions of our algorithms and evaluated their performance on a multi-core machine. The results show that the proposed table implementations are scalable and more efficient than any existing available alternative for in-memory realizations of a multi-index table.

We introduce a new distributed computing model called m&m that allows processes to both pass messages and share memory. Motivated by recent hardware trends, we find that this model improves the power of the pure message-passing and shared-memory models. As we demonstrate by example with two fundamental problems---consensus and eventual leader election---the added power leads to new algorithms that are more robust against failures and asynchrony. Our consensus algorithm combines the superior scalability of message passing with the higher fault tolerance of shared memory, while our leader election algorithms reduce the system synchrony needed for correctness. These results point to a wide new space for future exploration of other problems, techniques, and benefits.

Transactions are widely used in database engines and they becoming increasingly useful as a general synchronization technique for multicore machines [1]. Transactional systems allow a programmer to encapsulate multiple operations inside a transaction. All these operations appear to be executed atomically or not at all.

Non-volatile memory is expected to coexist with (or even displace) volatile DRAM for main memory in upcoming architectures. This has led to increasing interest in the problem of designing and specifying durable data structures that can recover from system crashes. Data structures may be designed to satisfy stricter or weaker durability guarantees to provide a balance between the strength of the provided guarantees and performance overhead. This paper proposes three novel implementations of a concurrent lock-free queue. These implementations illustrate algorithmic challenges in building persistent lock-free data structures with different levels of durability guarantees. In presenting these challenges, the proposed algorithmic designs, and the different durability guarantees, we hope to shed light on ways to build a wide variety of durable data structures. We implemented the various designs and compared their performance overhead to a simple queue design for standard (volatile) memory.

Concurrent data structures provide fundamental building blocks for concurrent programming. Standard concurrent data structures may be extended by allowing a sequence of operations to be submitted as a batch for later execution. A sequence of such operations can then be executed more efficiently than the standard execution of one operation at a time. In this paper we develop a novel algorithmic extension to the prevalent FIFO queue data structure that exploits such batching scenarios. An implementation in C++ on a multicore demonstrates a significant performance improvement of up to 16x (depending on batch lengths), compared to previous queue implementations.

Dynamic programming languages such as Python and Ruby are widely used, and much effort is spent on making them efficient. One substantial research effort in this direction is the enabling of parallel code execution. While there has been significant progress, making dynamic collections efficient, scalable, and thread-safe is an open issue. Typical programs in dynamic languages use few but versatile collection types. Such collections are an important ingredient of dynamic environments, but are difficult to make safe, efficient, and scalable. In this paper, we propose an approach for efficient and concurrent collections by gradually increasing synchronization levels according to the dynamic needs of each collection instance. Collections reachable only by a single thread have no synchronization, arrays accessed in bounds have minimal synchronization, and for the general case, we adopt the Layout Lock paradigm and extend its design with a lightweight version that fits the setting of dynamic languages. We apply our approach to Ruby's Array and Hash collections. Our experiments show that our approach has no overhead on single-threaded benchmarks, scales linearly for Array and Hash accesses, achieves the same scalability as Fortran and Java for classic parallel algorithms, and scales better than other Ruby implementations on Ruby workloads.

We propose a design for a fine-grained lock-based skiplist optimized for Graphics Processing Units (GPUs). While GPUs are often used to accelerate streaming parallel computations, it remains a significant challenge to efficiently offload concurrent computations with more complicated data-irregular access and fine-grained synchronization. Natural building blocks for such computations would be concurrent data structures, such as skiplists, which are widely used in general purpose computations. Our design utilizes array-based nodes which are accessed and updated by warp-cooperative functions, thus taking advantage of the fact that GPUs are most efficient when memory accesses are coalesced and execution divergence is minimized. The proposed design has been implemented, and measurements demonstrate improved performance of up to 11.6x over skiplist designs for the GPU existing today.

We identify a design pattern for concurrent data structures, called teleportation, that uses best- effort hardware transactional memory to speed up certain kinds of legacy concurrent data struc- tures. Teleportation unifies and explains several existing data structure designs, and it serves as the basis for novel approaches to reducing the memory traffic associated with fine-grained locking, and with hazard pointer management for memory reclamation.

State teleportation is a new technique for exploiting hardware transactional memory (HTM) to improve existing synchronization and memory management schemes for highly-concurrent data structures. When applied to fine-grained locking, a thread holding the lock for a node launches a hardware transaction that traverses multiple successor nodes, acquires the lock for the last node reached, and releases the lock on the starting node, skipping lock acquisitions for intermediate nodes. When applied to lock-free data structures, a thread visiting a node protected by a hazard pointer launches a hardware transaction that traverses multiple successor nodes, and publishes the hazard pointer only for the last node reached, skipping the memory barriers needed to publish intermediate hazard pointers. Experimental results show that these applications of state teleportation can substantially increase the performance of both lock-based and lock-free data structures.

Data-structures can benefit from dynamic data layout modifications when the size or the shape of the data structure changes during the execution, or when different phases in the program execute different workloads. However, in a modern multi-core environment, layout modifications involve costly synchronization overhead. In this paper we propose a novel layout lock that incurs a negligible overhead for reads and a small overhead for updates of the data structure. We then demonstrate the benefits of layout changes and also the advantages of the layout lock as its supporting synchronization mechanism for two data structures. In particular, we propose a concurrent binary search tree, and a concurrent array set, that benefit from concurrent layout modifications using the proposed layout lock. Experience demonstrates performance advantages and integration simplicity.

We propose a design for a fine-grained lock-based skiplist optimized for Graphics Processing Units (GPUs). While GPUs are often used to accelerate streaming parallel computations, it remains a significant challenge to efficiently offload concurrent computations with more complicated data-irregular access and fine-grained synchronization. Natural building blocks for such computations would be concurrent data structures, such as skiplists, which are widely used in general purpose computations. Our design utilizes array-based nodes which are accessed and updated by warp-cooperative functions, thus taking advantage of the fact that GPUs are most efficient when memory accesses are coalesced and execution divergence is minimized. The proposed design has been implemented, and measurements demonstrate improved performance of up to 2.6x over skiplist designs for the GPU existing today.

Non-volatile memory is expected to coexist with (or even displace) volatile DRAM for main memory in upcoming architectures. As a result, there is increasing interest in the problem of designing and specifying durable data structures that can recover from system crashes. Data-structures may be designed to satisfy stricter or weaker durability guarantees to provide a balance between the strength of the provided guarantees and performance overhead. This paper proposes three novel implementations of a concurrent lock-free queue. These implementations illustrate the algorithmic challenges in building persistent lock-free data structures with different levels of durability guarantees. We believe that by presenting these challenges, along with the proposed algorithmic designs, and the possible levels of durability guarantees, we can shed light on avenues for building a wide variety of durable data structures. We implemented the various designs and evaluate their performance overhead compared to a simple queue design for standard (volatile) memory.

Compaction of a managed heap is a costly operation to be avoided as much as possible in commercial runtimes. Instead, partial compaction is often used to defragment parts of the heap and avoid space blowup. Previous study of compaction limitation provided some initial asymptotic bounds but no implications for practical systems. In this work, we extend the theory to obtain better bounds and make them strong enough to become meaningful for modern systems.

Garbage collection may benefit greatly from knowledge about program behavior, but most managed languages do not provide means for the programmer to deliver such knowledge. In this work we propose a very simple interface that requires minor programmer effort and achieves substantial performance and scalability improvements. In particular, we focus on the common use of data structures or collections for organizing data on the heap. We let the program notify the collector which classes represent nodes of data structures and also when such nodes are being removed from their data structures. The data-structure aware (DSA) garbage collector uses this information to improve performance, locality, and load balancing. Experience shows that this interface requires a minor modification of the application. Measurements show that for some significant benchmarks this interface can dramatically reduce the time spent on garbage collection and also improve the overall program performance.

Lock-free data-structures are widely employed in practice, yet designing lock-free memory reclamation for them is notoriously difficult. In particular, all known lock-free reclamation schemes are ``manual'' in the sense that the developer has to specify when nodes have retired and may be reclaimed. Retiring nodes adequately is non-trivial and often requires the modification of the original lock-free algorithm. In this paper we present an automatic lock-free reclamation scheme for lock-free data-structures in the spirit of a mark-sweep garbage collection. The proposed algorithm works with any normalized lock-free algorithm and with no need for the programmer to retire nodes or make changes to the algorithm. Evaluation of the proposed scheme on a linked-list and a hash table shows that it performs similarly to the best manual (lock-free) memory reclamation scheme.

A fundamental challenge in designing concurrent data structures is obtaining efficient wait-free implementations, in which each operation completes regardless of the behavior of other operations in the system. The most common paradigm for guaranteeing wait-freedom is to employ a helping mechanism, in which, intuitively, fast processes help slow processes complete their operations. Curiously, despite its abundant use, to date, helping has not been formally defined nor was its necessity rigorously studied. In this paper we initiate a rigorous study of the interaction between wait-freedom and helping. We start with presenting a formal definition of help, capturing the intuition of one thread helping another to make progress. Next, we present families of object types for which help is necessary in order to obtain wait-freedom. In other words, we prove that for some types there are no linearizable wait-free help-free implementations. In contrast, we show that other, simple types, can be implemented in a linearizable wait-free manner without employing help. Finally, we provide a universal strong primitive for implementing wait-free data structures without using help. Specifically, given a wait-free help-free fetch&cons object, one can implement any type in a wait-free help-free manner.

Lock-free data structures achieve high responsiveness, aid scalability, and avoid deadlocks and livelocks. But providing memory management support for such data structures without foiling their progress guarantees is difficult. Often, designers employ the hazard pointers technique, which may impose a high performance overhead.

Lock-free data structures guarantee overall system progress, whereas wait-free data structures guarantee the progress of each and every thread, providing the desirable non-starvation guarantee for concurrent data structures. While practical lock-free implementations are known for various data structures, wait-free data structure designs are rare. Wait-free implementations have been notoriously hard to design and often inefficient. In this work we present a transformation of lock-free algorithms to wait-free ones allowing even a non-expert to transform a lock-free data-structure into a practical wait-free one. The transformation requires that the lock-free data structure is given in a normalized form defined in this work. Using the new method, we have designed and implemented wait-free linked-list, skiplist, and tree and we measured their performance. It turns out that for all these data structures the wait-free implementations are only a few percent slower than their lock-free counterparts, while still guaranteeing non-starvation.

Compaction of a managed heap is considered a costly operation, and is avoided as much as possible in commercial runtimes. Instead, partial compaction is often used to defragment parts of the heap and avoid space blow up. Previous study of compaction limitation provided some initial asymptotic bounds but no implications for practical systems. In this work, we extend the theory to obtain better bounds and make them strong enough to become meaningful for modern systems.

Efficient memory management of dynamic non-blocking data structures remains an important open question. Existing methods either sacrifice the ability to deallocate objects or reduce performance notably. In this paper, we present a novel technique, called Drop the Anchor, which significantly reduces the overhead associated with the memory management while reclaiming objects even in the presence of thread failures. We demonstrate this memory management scheme on the common linked list data structure. Using extensive evaluation, we show that Drop the Anchor significantly outperforms Hazard Pointers, the widely used technique for non-blocking memory management.

Lock-freedom is a progress guarantee that ensures overall program progress. Wait-freedom is a stronger progress guarantee that ensures the progress of each thread in the program. While many practical lock-free algorithms exist, wait-free algorithms are typically inefficient and hardly used in practice. In this paper, we propose a methodology called fast-path-slow-path for creating efficient wait-free algorithms. The idea is to execute the efficient lock-free version most of the time and revert to the wait-free version only when things go wrong. The generality and effectiveness of this methodology is demonstrated by two examples. In this paper, we apply this idea to a recent construction of a wait-free queue, bringing the wait-free implementation to perform in practice as efficient as the lock-free implementation. In another work, the fast-path-slow-path methodology has been used for (dramatically) improving the performance of a wait-free linked-list.

The linked-list data structure is fundamental and ubiquitous. Lock-free versions of the linked-list are well known. However, the existence of a practical wait-free linked-list has been open. In this work we designed such a linked-list. To achieve better performance, we have also extended this design using the fast-path-slow-path methodology. The resulting implementation achieves performance which is competitive with that of Harris's lock-free list, while still guaranteeing non-starvation via wait-freedom. We have also developed a proof for the correctness and the wait-freedom of our design.

Lock-free data structures provide a progress guarantee and are known for facilitating scalability, avoiding deadlocks and livelocks, and providing guaranteed system responsiveness. In this paper we present a design for a lock-free balanced tree, specifically, a B+tree. The B+tree data structure has an important practical applications, and is used in various storage-system products. As far as we know this is the first design of a lock-free, dynamic, and balanced tree, that employs standard compare-and-swap operations.

Dynamic memory allocation is ubiquitous in today's runtime environments. Allocation and deallocation of objects during program execution may cause fragmentation and foil the program's ability to allocate objects. Robson [1971] has shown that a worst-case scenario can create a space overhead within a factor of log n of the space that is actually required by the program, where n is the size of the largest possible object. Compaction can eliminate fragmentation, but is too costly to be run frequently. Many runtime systems employ partial compaction, in which only a small fraction of the allocated objects are moved. Partial compaction reduces some of the existing fragmentation at an acceptable cost. In this article we study the effectiveness of partial compaction and provide the first rigorous lower and upper bounds on its effectiveness in reducing fragmentation at a low cost.

Dynamic memory allocation is ubiquitous in today's runtime environments. Allocation and de-allocation of objects during program execution may cause fragmentation and foil the program's ability to allocate objects. Robson has shown that a worst case scenario can create a space overhead within a factor of log(n) of the space that is actually required by the program, where n is the size of the largest possible object. Compaction can eliminate fragmentation, but is too costly to be run frequently. Many runtime systems employ partial compaction, in which only a small fraction of the allocated objects are moved. Partial compaction reduces some of the existing fragmentation at an acceptable cost. In this paper we study the effectiveness of partial compaction and provide the first rigorous lower and upper bounds on its effectiveness in reducing fragmentation at a low cost.

The queue data structure is fundamental and ubiquitous. Lock-free versions of the queue are well known. However, an important open question is whether practical wait-free queues exist. Until now, only versions with limited concurrency were proposed. In this paper we provide a design for a practical wait-free queue. Our construction is based on the highly efficient lock-free queue of Michael and Scott. To achieve wait-freedom, we employ a priority-based helping scheme in which faster threads help the slower peers to complete their pending operations. We have implemented our scheme on multicore machines and present performance measurements comparing our implementation with that of Michael and Scott in several system configurations.

In this paper, we study the question of whether or not it is possible to construct protocols for general secure computation in the setting of malicious adversaries and no honest majority that use the underlying primitive (e.g., enhanced trapdoor permutation) in a black-box way only. Until now, all known general constructions for this setting were inherently non-black-box since they required the parties to prove zero-knowledge statements that are related to the computation of the underlying primitive. Our main technical result is a fully black-box reduction from oblivious transfer with security against malicious parties to oblivious transfer with security against semihonest parties. As a corollary, we obtain the first constructions of general multiparty protocols (with security against malicious adversaries and without an honest majority) which make only a black-box use of semihonest oblivious transfer, or alternatively a black-box use of lower-level primitives such as enhanced trapdoor permutations or homomorphic encryption. In order to construct this reduction we introduce a new notion of security called privacy in the presence of defensible adversaries. This notion states that if an adversary can produce (retroactively, after the protocol terminates) an input and random tape that make its actions appear to be honest, then it is guaranteed that it learned nothing more than its prescribed output. We then show how to construct defensible oblivious transfer from semihonest oblivious transfer, and malicious oblivious transfer from defensible oblivious transfer, all in a black-box way.

Two settings are traditionally considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Existing protocols that assume an honest majority provide “full security” (and, in particular, guarantee output delivery and fairness) when this assumption holds, but are completely insecure if this assumption is violated. On the other hand, known protocols tolerating an arbitrary number of corruptions do not guarantee fairness or output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the “best of both worlds”: namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Here, we rule out this possibility (at least for general functionalities) and show some positive results regarding what can be achieved.

The pervasiveness of multiprocessor and multicore hardware and the rising level of available parallelism are radically changing the computing landscape. Can software deal with tomorrow's potential higher parallelism? In this paper we study this issue from the garbage collection perspective. In particular, we investigate the scalability of parallel heap tracing, which stands at the core of the garbage collection activity. Heap shapes can be sequential in nature, and prevent the collector from scaling the trace. We start by proposing the idealized trace utilization as a scalability measure for evaluating the scalability of a given heap shape. We then examine standard Java benchmarks and evaluate the existence of non-scalable object-graph shapes in their execution. Next, we propose and implement a prototype of garbage collection techniques that attempt to ameliorate the object-graph shape problem. Finally, we measure and report their efficacy.

Parallel platforms are becoming ubiquitous with modern computing systems. Many parallel applications attempt to avoid locks in order to achieve high responsiveness, aid scalability, and avoid deadlocks and livelocks. However, avoiding the use of system locks does not guarantee that no locks are actually used, because progress inhibitors may occur in subtle ways through various program structures. Notions of progress guarantee such as lock-freedom, wait-freedom, and obstruction-freedom have been proposed in the literature to provide various levels of progress guarantees.

Garbage collectors are notoriously hard to verify, due to their low-level interaction with the underlying system and the general difficulty in reasoning about reachability in graphs. Several papers have presented verified collectors, but either the proofs were hand-written or the collectors were too simplistic to use on practical applications. In this work, we present two mechanically verified garbage collectors, both practical enough to use for real-world C# benchmarks. The collectors and their associated allocators consist of x86 assembly language instructions and macro instructions, annotated with preconditions, postconditions, invariants, and assertions. We used the Boogie verification generator and the Z3 automated theorem prover to verify this assembly language code mechanically. We provide measurements comparing the performance of the verified collector with that of the standard Bartok collectors on off-the-shelf C# benchmarks, demonstrating their competitiveness.

Two major efficiency parameters for garbage collectors are the throughput overheads and the pause times that they introduce. Highly responsive systems need to use collectors with as short as possible pause times. Pause lengths have decreased significantly during the years, especially through the use of concurrent garbage collectors. For modern concurrent collectors, the longest pause is typically created by the need to atomically scan the runtime stack. All practical concurrent collectors that we are aware of must obtain a snapshot of the pointers on each thread’s runtime stack, in order to reclaim objects correctly. To further reduce the length of the collector pauses, incremental stack scans were proposed. However, previous such methods employ locks to stop the mutator from accessing a stack frame while it is being scanned. Thus, these methods introduce a potential long and unpredictable pauses for a mutator thread. In this work we propose the first concurrent, incremental, and lock-free stack scanning for garbage collectors, allowing high responsiveness and support for programs that employ fine-synchronization to avoid locks. Our solution can be employed by all concurrent collectors that we are aware of, it is lock-free, it imposes a negligible overhead on the program execution, and it supports the special in-stack references existing in languages like C#.

As garbage collected languages become widely used, the quest for reducing collection overheads becomes essential. In this paper, we propose a compiler optimization called path specialization that shrinks the cost of memory barriers for a wide variety of garbage collectors including concurrent, incremental, and real-time collectors. Path specialization provides a non-trivial decrease in write-barrier overheads and a drastic reduction of read-barrier overheads. It is effective when used with collectors that go through various phases each employing a different barrier behavior, and is most effective for collectors that have an idle phase, in which no barrier activity is required. We have implemented path specialization in the Bartok compiler and runtime for C# and tested it with state-of-the-art concurrent and real-time collectors, demonstrating its efficacy.

Concurrent garbage collection is highly attractive for real-time systems, because offloading the collection effort from the executing threads allows faster response, allowing for extremely short deadlines at the microseconds level. Concurrent collectors also offer much better scalability over incremental collectors. The main problem with concurrent real-time collectors is their complexity. The first concurrent real-time garbage collector that can support fine synchronization, STOPLESS, has recently been presented by Pizlo et al. In this paper, we propose two additional (and different) algorithms for concurrent real-time garbage collection: CLOVER and CHICKEN. Both collectors obtain reduced complexity over the first collector STOPLESS, but need to trade a benefit for it. We study the algorithmic strengths and weaknesses of CLOVER and CHICKEN and compare them to STOPLESS. Finally, we have implemented all three collectors on the Bartok compiler and runtime for C# and we present measurements to compare their efficiency and responsiveness.

We present Stopless: a concurrent real-time garbage collector suitable for modern multiprocessors running parallel multithreaded applications. Creating a garbage-collected environment that supports real-time on modern platforms is notoriously hard,especially if real-time implies lock-freedom. Known real-time collectors either restrict the real-time guarantees to uniprocessors only, rely on special hardware, or just give up supporting atomic operations (which are crucial for lock-free software). Stopless is the first collector that provides real-time responsiveness while preserving lock-freedom, supporting atomic operations, controlling fragmentation by compaction, and supporting modern parallel platforms. Stopless is adequate for modern languages such as C# or Java. It was implemented on top of the Bartok compiler and runtime for C# and measurements demonstrate high responsiveness (a factor of a 100 better than previously published systems), virtually no pause times, good mutator utilization, and acceptable overheads.

A reference-counting garbage collector cannot reclaim unreachable cyclic structures of objects. Therefore, reference-counting collectors either use a backup tracing collector infrequently, or employ a cycle collector to reclaim cyclic structures. We propose a new concurrent cycle collector, one that runs concurrently with the program threads, imposing negligible pauses (of around 1ms) on a multiprocessor. Our new collector combines a state-of-the-art cycle collector [Bacon and Rajan 2001] with sliding-views collectors [Levanoni and Petrank 2001, 2006; Azatchi et al. 2003]. The use of sliding views for cycle collection yields two advantages. First, it drastically reduces the number of cycle candidates, which in turn drastically reduces the work required to record and trace these candidates. Consequentially, a large improvement in cycle collection efficiency is achieved. Second, it eliminates the theoretical termination problem that appeared in the earlier concurrent cycle collector. There, a rare race may delay the reclamation of an unreachable cyclic structure forever. The sliding-views cycle collector guarantees reclamation of all unreachable cyclic structures. The proposed collector was implemented on the Jikes RVM and we provide measurements including a comparison between the use of backup tracing and the use of cycle collection with reference counting. To the best of our knowledge, such a comparison has not been reported before.

The widely used Mark-and-Sweep garbage collector has a drawback in that it does not move objects during collection. As a result, large long-running realistic applications, such as Web application servers, frequently face the fragmentation problem. To eliminate fragmentation, a heap compaction is run periodically. However, compaction typically imposes very long undesirable pauses in the application. While efficient concurrent collectors are ubiquitous in production runtime systems (such as JVMs), an efficient non-intrusive compactor is still missing.In this paper we present the Compressor, a novel compaction algorithm that is concurrent, parallel, and incremental. The Compressor compacts the entire heap to a single condensed area, while preserving the objects' order, but reduces pause times significantly, thereby allowing acceptable runs on large heaps. Furthermore, the Compressor is the first compactor that requires only a single heap pass. As such, it is the most efficient compactors known today, even when run in a parallel Stop-the-World manner (i.e., when the program threads are halted). Thus, to the best of our knowledge, the Compressor is the most efficient compactor known today. The Compressor was implemented on a Jikes Research RVM and we provide measurements demonstrating its qualities.

It is well known that the secure computation of non-trivial functionalities in the setting of no honest majority requires computational assumptions. We study the way such computational assumptions are used. Specifically, we ask whether the secure protocol can use the underlying primitive (e.g., one-way trapdoor permutation) in a black-box way, or must it be nonblack-box (by referring to the code that computes this primitive)? Despite the fact that many general constructions of cryptographic schemes (e.g., CPA-secure encryption) refer to the underlying primitive in a black-box way only, there are some constructions that are inherently nonblack-box. Indeed, all known constructions of protocols for general secure computation that are secure in the presence of a malicious adversary and without an honest majority use the underlying primitive in a nonblack-box way (requiring to prove in zero-knowledge statements that relate to the primitive).In this paper, we study whether such nonblack-box use is essential. We present protocols that use only black-box access to a family of (enhanced) trapdoor permutations or to a homomorphic public-key encryption scheme. The result is a protocol whose communication complexity is independent of the computational complexity of the underlying primitive (e.g., a trapdoor permutation) and whose computational complexity grows only linearly with that of the underlying primitive. This is the first protocol to exhibit these properties.

Abstract We propose the use of generations with modern reference counting. A reference counting collector is well suited to collect the old generation, containing a large fraction of live objects that are modified infrequently. Such a collector can be combined with a tracing collector to collect the young generation, typically containing a small fraction of live objects. We have designed such a collector appropriate for running on a multiprocessor. As our building blocks, we used the sliding‐views on‐the‐fly collectors. We have implemented the new collector on the Jikes Research Java Virtual Machine (Jikes RVM) and compared it with the concurrent reference counting collector supplied with the Jikes RVM package. Our measurements demonstrate short pause times, retaining those of the original on‐the‐fly collectors and a gain in application throughput time. It turns out that a modern reference counting collector may benefit from the use of generations. Copyright © 2006 John Wiley & Sons, Ltd.

Reference-counting is traditionally considered unsuitable for multiprocessor systems. According to conventional wisdom, the update of reference slots and reference-counts requires atomic or synchronized operations. In this work we demonstrate this is not the case by presenting a novel reference-counting algorithm suitable for a multiprocessor system that does not require any synchronized operation in its write barrier (not even a compare-and-swap type of synchronization). A second novelty of this algorithm is that it allows eliminating a large fraction of the reference-count updates, thus, drastically reducing the reference-counting traditional overhead. This article includes a full proof of the algorithm showing that it is safe (does not reclaim live objects) and live (eventually reclaims all unreachable objects).We have implemented our algorithm on Sun Microsystems' Java Virtual Machine (JVM) 1.2.2 and ran it on a four-way IBM Netfinity 8500R server with 550-MHz Intel Pentium III Xeon and 2 GB of physical memory. Our results show that the algorithm has an extremely low latency and throughput that is comparable to the stop-the-world mark and sweep algorithm used in the original JVM.

Multithreaded applications with multigigabyte heaps running on modern servers provide new challenges for garbage collection (GC). The challenges for “server-oriented” GC include: ensuring short pause times on a multigigabyte heap while minimizing throughput penalty, good scaling on multiprocessor hardware, and keeping the number of expensive multicycle fence instructions required by weak ordering to a minimum.We designed and implemented a collector facing these demands building on the mostly concurrent garbage collector proposed by Boehm et al. [1991]. Our collector incorporates new ideas into the original collector. We make it parallel and incremental; we employ concurrent low-priority background GC threads to take advantage of processor idle time; we propose novel algorithmic improvements to the basic mostly concurrent algorithm improving its efficiency and shortening its pause times; and finally, we use advanced techniques, such as a low-overhead work packet mechanism to enable full parallelism among the incremental and concurrent collecting threads and ensure load balancing.We compared the new collector to the mature, well-optimized, parallel, stop-the-world mark-sweep collector already in the IBM JVM. When allowed to run aggressively, using 72% of the CPU utilization during a short concurrent phase, our collector prototype reduces the maximum pause time from 161 ms to 46 ms while only losing 11.5% throughput when running the SPECjbb2000 benchmark on a 600-MB heap on an 8-way PowerPC 1.1-GHz processors. When the collector is limited to a nonintrusive operation using only 29% of the CPU utilization, the maximum pause time obtained is 79 ms and the loss in throughput is 15.4%.

We propose a heap compaction algorithm appropriate for modern computing environments. Our algorithm is targeted at SMP platforms. It demonstrates high scalability when running in parallel but is also extremely efficient when running single-threaded on a uniprocessor. Instead of using the standard forwarding pointer mechanism for updating pointers to moved objects, the algorithm saves information for a pack of objects. It then does a small computation to process this information and determine each object's new location. In addition, using a smart parallel moving strategy, the algorithm achieves (almost) perfect compaction in the lower addresses of the heap, whereas previous algorithms achieved parallelism by compacting within several predetermined segments.

With concurrent and garbage collected languages like Java and C# becoming popular, the need for a suitable non-intrusive, efficient, and concurrent multiprocessor garbage collector has become acute. We propose a novel mark and sweep on-the-fly algorithm based on the sliding views mechanism of Levanoni and Petrank. We have implemented our collector on the Jikes Java Virtual Machine running on a Netfinity multiprocessor and compared it to the concurrent algorithm and to the stop-the-world collector supplied with Jikes JVM. The maximum pause time that we measured with our benchmarks over all runs was 2ms. In all runs, the pause times were smaller than those of the stop-the-world collector by two orders of magnitude and they were also always shorter than the pauses of the Jikes concurrent collector. Throughput measurements of the new garbage collector show that it outperforms the Jikes concurrent collector by up to 60%. As expected, the stop-the-world does better than the on-the-fly collectors with results showing about 10% difference.On top of being an effective mark and sweep on-the-fly collector standing on its own, our collector may also be used as a backup collector (collecting cyclic data structures) for the Levanoni-Petrank reference counting collector. These two algorithms perfectly fit sharing the same allocator, a similar data structure, and a similar JVM interface.

The mostly concurrent garbage collection was presented in the seminal paper of Boehm et al. With the deployment of Java as a portable, secure and concurrent programming language, the mostly concurrent garbage collector turned out to be an excellent solution for Java's garbage collection task. The use of this collector is reported for several modern production Java Virtual Machines and it has been investigated further in academia.In this paper, we present a modification of the mostly concurrent collector, which improves the throughput, the memory footprint, and the cache behavior of the collector without foiling the other good qualities (such as short pauses and high scalability). We implemented our solution on the IBM production JVM and obtained a performance improvement of up to 26.7%, a reduction in the heap consumption by up to 13.4%, and no substantial change in the (short) pause times. The modified algorithm was subsequently incorporated into the IBM production JVM.

The growing gap between the speed of memory access and cache access has made cache misses an influential factor in program efficiency. Much effort has been spent recently on reducing the number of cache misses during program run. This effort includes wise rearranging of program code, cache-conscious data placement, and algorithmic modifications that improve the program cache behavior. In this work we investigate the complexity of finding the optimal placement of objects (or code) in the memory, in the sense that this placement reduces the cache misses to the minimum. We show that this problem is one of the toughest amongst the interesting algorithmic problems in computer science. In particular, suppose one is given a sequence of memory accesses and one has to place the data in the memory so as to minimize the number of cache misses for this sequence. We show that if P ≠ NP, then one cannot efficiently approximate the optimal solution even up to a very liberal approximation ratio. Thus, this problem joins the small family of extremely inapproximable optimization problems. The other two famous members in this family are minimum coloring and maximum clique.

We show that any concurrent zero-knowledge protocol for a nontrivial language (i.e., for a language outside ${\cal BPP}$), whose security is proven via black-box simulation, must use at least $\tilde\Omega(\log n)$ rounds of interaction. This result achieves a substantial improvement over previous lower bounds and is the first bound to rule out the possibility of constant-round concurrent zero-knowledge when proven via black-box simulation. Furthermore, the bound is polynomially related to the number of rounds in the best known concurrent zero-knowledge protocol for languages in ${\cal NP}$ (which is established via black-box simulation).

Reference counting is not naturally suitable for running on multiprocessors. The update of pointers and reference counts requires atomic and synchronized operations. We present a novel reference counting algorithm suitable for a multiprocessor that does not require any synchronized operation in its write barrier (not even a compare-and-swap type of synchronization). The algorithm is efficient and may complete with any tracing algorithm.

We show that any concurrent zero-knowledge protocol for a non-trivial language (i.e., for a language outside $\BPP$), whose security is proven via black-box simulation, must use at least \tildeΩ(log n) rounds of interaction. This result substantially improves over previous lower bounds, and is the first bound to rule out the possibility of constant-round black-box concurrent zero-knowledge. Furthermore, the bound is polynomially related to the number of rounds in the best known concurrent zero-knowledge protocol for languages in ~$\NP$.

A proof is concurrent zero-knowledge if it remains zero-knowledge when many copies of the proof are run in an asynchronous environment, such as the Internet. Richardson and Kilian have shown that there exists a concurrent zero-knowledge proof for any language in NP, but with round complexity polynomial in the maximum number of concurrent proofs. In this paper, we present a concurrent zero-knowledge proof for all languages in NP with a poly-logarithmic round complexity: specifically, ω(log^2 k) rounds given at most k concurrent proofs. Finally, we show that a simple modification of our proof is a resettable zero-knowledge proof for NP, with ω(log^2 k) rounds; previously known protocols required a polynomial number of rounds.

Java uses garbage collection (GC) for the automatic reclamation of computer memory no longer required by a running application. GC implementations for Java Virtual Machines (JVM) are typically designed for single processor machines, and do not necessarily perform well for a server program with many threads running on a multiprocessor. We designed and implemented an on-the-fly GC, based on the algorithm of Doligez, Leroy and Gonthier [13, 12] (DLG), for Java in this environment. An on-the-fly collector, a collector that does not stop the program threads, allows all processors to be utilized during collection and provides uniform response times. We extended and adapted DLG for Java (e.g., adding support for weak references) and for modern multiprocessors without sequential consistency, and added performance improvements (e.g., to keep track of the objects remaining to be traced). We compared the performance of our implementation with stop-the-world mark-sweep GC. Our measurements show th...

An on-the-fly garbage collector does not stop the program threads to perform the collection. Instead, the collector executes in a separate thread (or process) in parallel to the program. On-the-fly collectors are useful for multi-threaded applications running on multiprocessor servers, where it is important to fully utilize all processors and provide even response time, especially for systems for which stopping the threads is a costly operation.

We consider the question: Is finding just a part of a solution easier than finding the full solution? For example, is finding only an /spl epsiv/ fraction of the bits in a satisfying assignment to a 3-CNF formula easier than computing the whole assignment? For several important problems in NP we show that obtaining only a small fraction of the solution is as hard as finding the full solution. This can be interpreted in two ways: On the positive side, it is enough to look for an efficient algorithm that only recovers a small part of the solution, in order to completely solve any of these problems. On the negative side, any partial solution to these problems may be hard to find Some of our results can also be interpreted as robust proofs of membership.

Consider the set ℋ of all linear (or affine) transformations between two vector spaces over a finite field F . We study how good ℋ is as a class of hash functions, namely we consider hashing a set S of size n into a range having the same cardinality n by a randomly chosen function from ℋ and look at the expected size of the largest hash bucket. ℋ is a universal class of hash functions for any finite field, but with respect to our measure different fields behave differently. If the finite field F has n elements, then there is a bad set S ⊂ F 2 of size n with expected maximal bucket size Ω( n 1/3 ). If n is a perfect square, then there is even a bad set with largest bucket size always at least √n. (This is worst possible, since with respect to a universal class of hash functions every set of size n has expected largest bucket size below √ + 1/2.) If, however, we consider the field of two elements, then we get much better bounds. The best previously known upper bound on the expected size of the largest bucket for this class was O (2 √ log n ). We reduce this upper bound to O (log n log log n ). Note that this is not far from the guarantee for a random function. There, the average largest bucket would be Θ (log n / log log n ). In the course of our proof we develop a tool which may be of independent interest. Suppose we have a subset S of a vector space D over Z 2 , and consider a random linear mapping of D to a smaller vector space R . If the cardinality of S is larger than c ε | R |log| R |, then with probability 1 - ϵ, the image of S will cover all elements in the range.

We consider zero knowledge interactive proofs in a richer, more realistic communication environment. In this setting, one may simultaneously engage in many interactive proofs, and these proofs may take place in an asynchronous fashion. It is known that zero-knowledge is not necessarily preserved in such an environment; we show that for a large class of protocols, it cannot be preserved. Any 4 round (computational) zero-knowledge interactive proof (or argument) for a non-trivial language L is not black-box simulatable in the asynchronous setting.

We consider the combination of card marking with remembered sets for generational garbage collection as suggested by Hosking and Hudson [3]. When more than two generations are used, a naive implementation may cause excessive and wasteful scanning of the cards and thus increase the collection time. We offer a simple data structure and a corresponding algorithm to keep track of which cards need be scanned for which generation. We then extend these ideas for the Train Algorithm of [4]. Here, the solution is more involved, and allows tracking of which card should be scanned for which car-collection in the train.

We study the computational complexity of languages which have interactive proofs of logarithmic knowledge complexity. We show that all such languages can be recognized in ${\cal BPP}^{\cal NP}$. Prior to this work, for languages with greater-than-zero knowledge complexity only trivial computational complexity bounds were known. In the course of our proof, we relate statistical knowledge complexity to perfect knowledge complexity; specifically, we show that, for the honest verifier, these hierarchies coincide up to a logarithmic additive term.

We construct PCPS with strong zero-knowledge properties.First, we construct polynomially bounded (in size) PCP'S for NP which can be checked using poly-Iogarithmic queries, with polynomially low error, yet are statistical zero-knowledge against an adversary that makes U arbitrary queries, where U can be set to any polynomial.Second, we construct PCPS for NEXPTIME that can be checked using polynomially many queries, yet are statistically zero-knowledge against any polynomial y bounded adversary.These PCPS are exponential in size and have exponentially low error.Previously, it was only known how to construct zero-knowledge PCPS with a constant error probability.In the course of constructing these PCP'S we abstract a tool we call locking systems.We provide the definition and also a locking system with very efficient parameters.This mechanism may be useful in other settings as well.

We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem code equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not collapse, code equivalence is not NP-complete. On the other hand, we present a polynomial-time reduction from the graph isomorphism problem to code equivalence. Thus if one could find an efficient (i.e., polynomial-time) algorithm for code equivalence, then one could settle the long-standing problem of determining whether there is an efficient algorithm for solving graph isomorphism.

The authors show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class /spl Ascr//spl Mscr//spl cap/co-/spl Ascr//spl Mscr/. Thus, if the polynomial time hierarchy does not collapse, then /spl Nscr//spl Pscr/-complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict /spl Nscr//spl Pscr/ languages being proven with even one bit of knowledge. Next, they consider the relation between the error probability and the knowledge complexity of an interactive proof. They show that if the error probability /spl epsiv/(n) is less than 2/sup -3k(n)/ (where k(n) is the knowledge complexity) then the language proven has to be in the third level of the polynomial time hierarchy. In order to prove their main result, they develop an /spl Ascr//spl Mscr/ protocol for checking that a samplable distribution has a given entropy. They believe that this protocol is of independent interest.

We study the computational complexity of languages which have interactive proofs of logarithmic knowledge complexity.We show that all such languages can be recognized in B7VN7.Prior to this work, for languages with greaterthan-zero knowledge complexity (and specifically, even for knowledge complexity 1) only trivial computational complexity bounds (i.e., only recognizability in PSPAC& = ZP) were known.Inthe course of our proof, we relate statistical knowledge-complexity with perfect knowledge-complexity; specifically, we show that, for the honest verifier, these hierarchies coincide, up to a logarithmic additive term (i.e., sKc(k(.))g Pxc(k($) + log(.))).

We look at the question of how powerful a prover must be to give a zero-knowledge proof.We present the first unconditional bounds on the complexity of a statistical ZK prover.The result is that if a language possesses a statistical zero-knowledge then it also possesses a statistical zero-knowledge proof in which the prover runs in probabilistic, polynomial time with an NP oracle.Previously this was only known given the existence of one-way permutations.Extending these techniques to protocols of knowledge complexity k(n) >0, we derive bounds on the time complexity of languages of "small" knowledge complexity.Underlying these results is a technique for efficiently generating an "almost" random element of a set S E P.Namely, we construct a probabilistic machine with an NP oracle which, on input 1" and 6 > 0 runs in time polynomial in n and lg 6-1, and outputs a random string from a distribution within distance 6 of the uniform distribution on S n {O, l}~.

Several alternative ways of defining knowledge complexity are presented, and the relationships between them are explored. The discussion covers inclusion results, separation results, properties of knowledge complexity of languages in the Hint sense, and the knowledge complexity of constant round AM proofs.>