Tight Bounds for Critical Sections in Processor Consistent Platforms

Most weak memory consistency models are incapable of supporting a solution to mutual exclusion using only read and write operations to shared variables. Processor Consistency-Goodman's version (PC-G) is an exception. Ahamad et al. showed that Peterson's mutual exclusion algorithm is correct for PC-G, but Lamport's bakery algorithm is not. This paper derives a lower bound on the number of and type of (single or multiwriter) variables that a mutual exclusion algorithm must use in order to be correct for PC-G. Specifically, any such solution for n processes must use at least one multiwriter variable and n single-writer variables. Peterson's algorithm for two processes uses one multiwriter and two single-writer variables, and therefore establishes that this bound is tight for two processes. This paper presents a new n{hbox{-}}{rm{process}} algorithm for mutual exclusion that is correct for PC-G and achieves the bound for any n. While Peterson's algorithm is fair, this extension to arbitrary n is not fair. Six known algorithms that use the same number and type of variables are shown to fail to guarantee mutual exclusion when the memory consistency model is only PC-G, as opposed to the Sequential Consistency model for which they were designed. A corollary of our investigation is that, in contrast to Sequential Consistency, multiwriter variables cannot be implemented from single-writer variables in a PC-G system.     

Asynchronous group mutual exclusion

Abstract. Mutual exclusion and concurrency are two fundamental and essentially opposite features in distributed systems. However, in some applications such as Computer Supported Cooperative Work (CSCW) we have found it necessary to impose mutual exclusion on different groups of processes in accessing a resource, while allowing processes of the same group to share the resource. To our knowledge, no such design issue has been previously raised in the literature. In this paper we address this issue by presenting a new problem, called Congenial Talking Philosophers, to model group mutual exclusion. We also propose several criteria to evaluate solutions of the problem and to measure their performance. Finally, we provide an efficient and highly concurrent distributed algorithm for the problem in a shared-memory model where processes communicate by reading from and writing to shared variables. The distributed algorithm meets the proposed criteria, and has performance similar to some naive but centralized solutions to the problem. Received: November 1998 / Accepted: April 2000     

The congenial talking philosophers problem in computer networks

Summary. Group mutual exclusion occurs naturally in situations where a resource can be shared by processes of the same group, but not by processes of different groups. For example, suppose data is stored in a CD-jukebox. Then when a disc is loaded for access, users that need data on the disc can concurrently access the disc, while users that need data on a different disc have to wait until the current disc is unloaded. The design issues for group mutual exclusion have been modeled as the Congenial Talking Philosophers problem, and solutions for shared-memory models have been proposed [12,14]. As in ordinary mutual exclusion and many other problems in distributed systems, however, techniques developed for shared memory do not necessary apply to message passing (and vice versa). So in this paper we investigate solutions for Congenial Talking Philosophers in computer networks where processes communicate by asynchronous message passing. We first present a solution that is a straightforward adaptation from Ricart and Agrawala's algorithm for ordinary mutual exclusion. Then we show that the simple modification suffers a severe performance degradation that could cause the system to behave as though only one process of a group can be in the critical section at a time. We then present a more efficient and highly concurrent distributed algorithm for the problem, the first such solution in computer networks. Received: August 2000 / Accepted: November 2001     

Space-efficient FCFS group mutual exclusion

In the group mutual exclusion problem [Y. Joung, Asynchronous group mutual exclusion, Distrib. Comput. 13 (2000) 189], which generalizes mutual exclusion [E. Dijkstra, Solution of a problem in concurrent programming control, Comm. ACM 8 (9) (1965) 569], a process chooses a session when it requests entry into the Critical Section. A group mutual exclusion algorithm must ensure that the mutual exclusion property holds: if two processes are in the Critical Section at the same time, then they request the same session. In addition to mutual exclusion, lockout freedom, bounded exit, and concurrent entering are basic properties that are desirable in any group mutual exclusion algorithm.Hadzilacos in [Proc. 20th Annual Symp. on Principles of Distributed Computing, 2001, pp. 100-106] first introduced a fairness condition, called first-come-first-served (FCFS), for group mutual exclusion. The only known FCFS group mutual exclusion algorithm is due to Hadzilacos [Proc. 20th Annual Symp. on Principles of Distributed Computing, 2001, pp. 100-106], and requires Θ(N²) bounded shared registers, where N is the number of processes. We present a FCFS group mutual exclusion algorithm that uses only Θ(N) bounded shared registers. (The existence of such an algorithm was posed as an open problem by Hadzilacos.)     

Nonatomic dual bakery algorithm with bounded tokens

A simple mutual exclusion algorithm is presented that only uses nonatomic shared variables of bounded size, and that satisfies bounded overtaking. When the shared variables behave atomically, it has the first-come-first-served property (FCFS). Nonatomic access makes information vulnerable. The effects of this can be mitigated by minimizing the information and by spreading it over more variables. The design approach adopted here begins with such mitigating efforts. These resulted in an algorithm with a proof of correctness, first for atomic variables. This proof is then used as a blueprint for the simultaneous development of the algorithm for nonatomic variables and its proof. Mutual exclusion is proved by means of invariants. Bounded overtaking and liveness under weak fairness are proved with invariants and variant functions. Liveness under weak fairness is formalized and proved in a set-theoretic version of temporal logic. All these assertions are verified with the proof assistant PVS. We heavily rely on the possibility offered by a proof assistant like PVS to reuse proofs developed for one context in a different context.     

Approximated parameterized verification of infinite-state processes with global conditions

We present a simple and effective approximated backward reachability procedure for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. The procedure operates on an over-approximation of the transition system induced by the parameterized system. We verify mutual exclusion for complex protocols such as atomic, non-atomic and distributed versions of Lamport’s bakery algorithm.     

Closing the complexity gap between FCFS mutual exclusion and mutual exclusion

First-Come-First-Served (FCFS) mutual exclusion (ME) is the problem of ensuring that processes attempting to concurrently access a shared resource do so one by one, in a fair order. In this paper, we close the complexity gap between FCFS ME and ME in the asynchronous shared memory model where processes communicate using atomic reads and writes only, and do not fail. Our main result is the first known FCFS ME algorithm that makes O(log N) remote memory references (RMRs) per passage and uses only atomic reads and writes. Our algorithm is also adaptive to point contention. More precisely, the number of RMRs a process makes per passage in our algorithm is Θ(min(k, log N)), where k is the point contention. Our algorithm matches known RMR complexity lower bounds for the class of ME algorithms that use reads and writes only, and beats the RMR complexity of prior algorithms in this class that have the FCFS property.     

Automatic verification for a class of distributed systems

Summary. The paper presents a new analysis method for a class of concurrent systems which are formed of several interacting components with the same structure. The model for these systems is composed of a control process and a set of homogeneous user processes. The control and user processes are modeled by finite labeled state transition systems which interact by means of enabling functions and triggering mechanisms. Based on this structure, an analysis method is presented which allows system properties, derived by reachability analysis for a finite number of user processes, to be generalized to an arbitrary number of user processes. A procedure for the automatic verification of properties such as mutual exclusion and absence of deadlocks is presented and is then used to provide for the first time a fully automated verification of the Lamport's fast mutual exclusion algorithm. Received: October 1998/Accepted January 2000     

A Simulation Study on Distributed Mutual Exclusion

In the problem of mutual exclusion, concurrent access to a shared resource using a structural program abstraction called acritical section(CS) must be synchronized such that at any time only one process can enter the CS. In a distributed system, due to the lack of both a shared memory and a global clock, and due to unpredictable message delay, the design of a distributed mutual exclusion algorithm that is free from deadlock and starvation is much more complex than that in a centralized system. Based on different assumptions about communication topologies and a widely varying amount of information maintained by each site about other sites, several distributed mutual exclusion algorithms have been proposed. In this paper, we suvrey and analyze several well-known distributed mutual exclusion algorithms according to their related characteristics. We also compare the performance of these algorithms by a simulation study. Finally, we present a comparative analysis of these algorithms.     

Randomized mutual exclusion on a multiple access channel

In this paper we consider the mutual exclusion problem on a multiple access channel. Mutual exclusion is one of the fundamental problems in distributed computing. In the classic version of this problem, n processes execute a concurrent program that occasionally triggers some of them to use shared resources, such as memory, communication channel, device, etc. The goal is to design a distributed algorithm to control entries and exits to/from the shared resource (also called a critical section), in such a way that at any time, there is at most one process accessing it. In our considerations, the shared resource is the shared communication channel itself (multiple access channel), and the main challenge arises because the channel is also the only mean of communication between these processes. We consider both the classic and a slightly weaker version of mutual exclusion, called \(\varepsilon \)-mutual-exclusion, where for each period of a process staying in the critical section the probability that there is some other process in the critical section is at most \(\varepsilon \). We show that there are channel settings, where the classic mutual exclusion is not feasible even for randomized algorithms, while the \(\varepsilon \)-mutual-exclusion is. In more relaxed channel settings, we prove an exponential gap between the makespan complexity of the classic mutual exclusion problem and its weaker \(\varepsilon \)-exclusion version. We also show how to guarantee fairness of mutual exclusion algorithms, i.e., that each process that wants to enter the critical section will eventually succeed.     

A tight bound on remote reference time complexity of mutual exclusion in the read-modify-write model

In distributed shared memory multiprocessors, remote memory references generate processor-to-memory traffic, which may result in a bottleneck. It is therefore important to design algorithms that minimize the number of remote memory references. We establish a lower bound of three on remote reference time complexity for mutual exclusion algorithms in a model where processes communicate by means of a general read-modify-write primitive that accesses at most one shared variable in one instruction. Since the general read-modify-write primitive is a generalization of a variety of atomic primitives that have been implemented in multiprocessor systems, our lower bound holds for all mutual exclusion algorithms that use such primitives. Furthermore, this lower bound is shown to be tight by presenting an algorithm with the matching upper bound.     

Verifying a simplification of mutual exclusion by Lycklama–Hadzilacos

A simplification of the mutual exclusion algorithm of Lycklama and Hadzilacos (ACM Trans Program Lang Syst 13:558–576, 1991) is presented. It uses only four nonatomic shared bits per thread to guarantee mutual exclusion with the first-come-first-served property. The algorithm is verified by assertional methods, aided by the proof assistant PVS. A variation with five bits per thread is also given. This variation may give better performance when the number of threads is large. The use of the proof assistant made it easy to transfer the proof of the main algorithm to the variation.     

A simple local-spin group mutual exclusion algorithm

This paper presents a new solution to the group mutual exclusion problem recently posed by Joung. In this problem, processes repeatedly request access to various “sessions.” It is required that distinct processes are not in different sessions concurrently, that multiple processes may be in the same session concurrently, and that each process that tries to enter a session is eventually able to do so. This problem is a generalization of the mutual exclusion and readers-writers problems. Our algorithm and its correctness proof are substantially simpler than Joung's. This simplicity is achieved by building upon known solutions to the more specific mutual exclusion problem. Our algorithm also has various advantages over Joung's, depending on the choice of mutual exclusion algorithm used. These advantages include admitting a process to its session in constant time in the absence of contention, spinning locally in Cache Coherent (CC) and Nonuniform Memory Access (NUMA) systems, and improvements in the complexity measures proposed by Joung     

Randomized mutual exclusion with sub-logarithmic RMR-complexity

Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. Attiya, Hendler, and Woelfel (40th STOC, 2008) established an Ω(log N) lower bound on the number of RMRs incurred by processes as they enter and exit the critical section, where N is the number of processes in the system. This matches the upper bound of Yang and Anderson (Distrib. Comput. 9(1):51–60, 1995). The upper and lower bounds apply for algorithms that only use read and write operations. The lower bound of Attiya et al., however, only holds for deterministic algorithms. The question of whether randomized mutual exclusion algorithms, using reads and writes only, can achieve sub-logarithmic expected RMR complexity remained open. We answer this question in the affirmative by presenting starvation-free randomized mutual exclusion algorithms for the cache coherent (CC) and the distributed shared memory (DSM) model that have sub-logarithmic expected RMR complexity against the strong adversary. More specifically, each process incurs an expected number of O(log N / log log N) RMRs per passage through the entry and exit sections, while in the worst case the number of RMRs is O(log N).     

一种广域网中的分布式互斥算法

广域网可简单地看作由多个局域网通过远程通信线路互连组成。为了适应广域网环境的特点,文章提出了一种两层结构的分布式互斥算法模型,把广域网系统组织成由局部进程组成的局部网络的由每个局部网络中的协调进程组成的全局两层。为了互斥地访问共享资源,局部进程必须首先获得局部令牌,然后再向本地协调进程申请全局令牌,只有获得了局部和全避令牌的局部进程才能进入临界区。还讨论了对该算法可能的扩展。     

SELF-STABILIZING DEPTH-FIRST MULTI-TOKEN CIRCULATION IN TREE NETWORKS

Self stabilization is one of the new paradigms to investigate fault tolerance in distributed algorithm design. The multi-token or the l-exclusion problem is the logical generalization of standard mutual exclusion problem where l processes can enter their critical section at the same time. Self stabilizing single token circulation or the standard mutual exclusion problem has been investigated by a number of authors; recently authors in [16] have proposed a self stabilizing multi-token protocol for the ring networks. We propose a new self stabilizing algorithm (protocol) for depth first circulation of multiple tokens in a tree network. The algorithm uses only bounded integers and the correctness is proved by using induction.     

A Token-Based Distributed Group Mutual Exclusion Algorithm with Quorums

The group mutual exclusion problem is a generalization of mutual exclusion problem such that a set of processes in the same group can enter critical section simultaneously. In this paper, we propose a distributed algorithm for the group mutual exclusion problem in asynchronous message passing distributed systems. Our algorithm is based on tokens, and a process that obtains a token can enter critical section. For reducing message complexity, it uses coterie as a communication structure when a process sends a request messages. Informally, coterie is a set of quorums, each of which is a subset of the process set, and any two quorums share at least one process. The message complexity of our algorithm is $O(|Q|)$ in the worst case, where $|Q|$ is a quorum size that the algorithm adopts. Performance of the proposed algorithm is presented by analysis and discrete event simulation. Especially, the proposed algorithm achieves high concurrency, which is a performance measure for the number of processes that can be in critical section simultaneously.     

Implementing sequentially consistent programs on processor consistent platforms

Designers of distributed algorithms typically assume strong memory consistency guarantees, but system implementations provide weaker guarantees for better performance and scalability. This motivates the study of how to implement programs designed for sequential consistency on platforms with weaker consistency models. Typically, such implementations are impossible using only read and write operations to shared variables. One variant of processor consistency originally proposed by Goodman and called here PC-G is an exception because it provides just enough consistency to implement mutual exclusion using only reads and writes. This paper investigates the existence of compilers to convert arbitrary programs that use shared read/write variables with sequentially consistent memory semantics, to programs that use read/write variables with PC-G consistency semantics. We first provide a simple program transformation, and prove that it correctly compiles any 2-process program to a PC-G memory system, while preserving wait-freedom. We next prove that even a substantial generalization of this transformation cannot be a compiler for even a very restricted class of 3-process programs. Even though our program transformation is not a general compiler for three or more processes, it does correctly transform some specific n-process programs. In particular, for the special case of the (necessarily randomized) Test&Set algorithm of Tromp and Vitanyi, our transformation extends to any number of processes, thus providing the first algorithm for expected wait-free Test&Set on any weak memory system, using only read/write variables.     

Synthesis of mutual exclusion solutions based on binary semaphores

A graphical form of the mutual exclusion problem is considered in which each vertex represents a process and each edge represents a mutual exclusion constraint between the critical sections of the processes associated with its endpoints. An edge semaphore solution for mutual exclusion problems is defined, and those graphs which are edge solvable are characterized in terms of both a forbidden subgraph and a graph grammar. Finally, an efficient algorithm is given which generates the entry and exit sections for all processes in an edge-solvable problem     

Long lived adaptive splitter and applications

Summary. Long-lived and adaptive implementations of mutual exclusion and renaming in the read/write shared memory model are presented. An implementation of a task is adaptive if the step complexity of any operation in the implementation is a function of the number of processes that take steps concurrently with the operation. The renaming algorithm assigns a new unique id in the range to any process whose initial unique name is taken from a set of size N, for an arbitrary N and where k is the number of processes that actually take steps or hold a name while the new name is being acquired. The step complexity of acquiring a new name is , while the step complexity of releasing a name is 1. The space complexity of the algorithm is where n is an upper bound on the number of processes that may be active at the same time (acquiring or holding new names), which could be N in the worst case. Both the system response time and the worst case number of operations per process in the presented mutual-exclusion algorithm are adaptive. Both algorithms rely on the basic building block of a long-lived and adaptive splitter. While the adaptive-splitter satisfies a slightly different set of properties than the Moir-Anderson splitter [MA95], it is adaptive and long-lived. In addition, the new splitter properties enable the construction of a non-blocking long-lived (2k-1)-renaming algorithm (which is optimal in the size of the new name space). We believe that the mechanisms introduced in our splitter implementation are interesting on their own, and might be used in other adaptive and long-lived constructions. Received: March 2000 / Accepted July 2001