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Abstract: The termination detection problem involves detecting whether an ongoing distributed computation has ceased all its activities. We investigate the termination detection problem in an asynchronous distributed system under the crash-recovery model. It has been shown that the problem is impossible to solve under the crash-recovery model in general. We identify two conditions under which the termination detection problem can be solved in a safe manner. We also propose algorithms to detect termination under the conditions identified. [Copyright &y& Elsevier]

An important problem in distributed systems is to detect termination of a distributed computation. A distributed computation is said to have terminated when all processes have become passive and all channels have become empty. We focus on two attributes of a termination detection algorithm. First, whether the distributed computation starts from a single process or from multiple processes: diffusing computation versus non-diffusing computation. Second, whether the detection algorithm should be initiated along with the computation or can be initiated any time after the computation has started: simultaneous initiation versus delayed initiation. We show that any termination detection algorithm for a diffusing computation can be transformed into a termination detection algorithm for a non-diffusing computation. We also demonstrate that any termination detection algorithm for simultaneous initiation can be transformed into a termination detection algorithm for delayed initiation. We prove the correctness of our transformations, and show that our transformations have only a small impact on the performance of the given termination detection algorithm. [ABSTRACT FROM AUTHOR]

Determining order relationship between events of a distributed computation is a fundamental problem in distributed systems which has applications in many areas including debugging, visualization, checkpointing and recovery. Fidge/Mattern’s vector-clock mechanism captures the order relationship using a vector of size N in a system consisting of N processes. As a result, it incurs message and space overhead of N integers. Many distributed applications use synchronous messages for communication. It is therefore natural to ask whether it is possible to reduce the timestamping overhead for such applications. In this paper, we present a new approach for timestamping messages and events of a synchronously ordered computation, that is, when processes communicate using synchronous messages. Our approach depends on decomposing edges in the communication topology into mutually disjoint edge groups such that each edge group either forms a star or a triangle. We show that, to accurately capture the order relationship between synchronous messages, it is sufficient to use one component per edge group in the vector instead of one component per process. Timestamps for events are only slightly bigger than timestamps for messages. Many common communication topologies such as ring, grid and hypercube can be decomposed into $${\lceil N/2 \rceil}$$ edge groups, resulting in almost 50% improvement in both space and communication overheads. We prove that the problem of computing an optimal edge decomposition of a communication topology is NP-complete in general. We also present a heuristic algorithm for computing an edge decomposition whose size is within a factor of two of the optimal. We prove that, in the worst case, it is not possible to timestamp messages of a synchronously ordered computation using a vector containing fewer than $${2 \lfloor N/6 \rfloor}$$ components when N ≥ 2. Finally, we show that messages in a synchronously ordered computation can always be timestamped in an offline manner using a vector of size at most $${\lfloor N/2 \rfloor}$$ . [ABSTRACT FROM AUTHOR]

Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems should be able to operate properly even in the presence of software faults. Monitoring the execution of a distributed system, and, on detecting a fault, initiating the appropriate corrective action is an important way to tolerate such faults. This gives rise to the predicate detection problem which requires finding whether there exists a consistent cut of a given computation that satisfies a given global predicate.Detecting a predicate in a computation is, however, an NP-complete problem in general. In order to ameliorate the associated combinatorial explosion problem, we introduce the notion of computation slice. Formally, the slice of a computation with respect to a predicate is a (sub)computation with the least number of consistent cuts that contains all consistent cuts of the computation satisfying the predicate. Intuitively, slice is a concise representation of those consistent cuts of a computation that satisfy a certain condition. To detect a predicate, rather than searching the state-space of the computation, it is much more efficient to search the state-space of the slice.We prove that the slice of a computation is uniquely defined for all predicates. We also present efficient algorithms for computing the slice for several useful classes of predicates. For an arbitrary predicate, we establish that the problem of computing the slice is NP-complete in general. Nonetheless, for such a predicate, we develop an efficient heuristic algorithm for computing anapproximateslice. Our experimental results demonstrate that slicing can lead to an exponential improvement over existing techniques for predicate detection in terms of time and space. [ABSTRACT FROM AUTHOR]

Analyzing a distributed computation is a hard problem in general due to the combinatorial explosion in the size of the state-space with the number of processes in the system. By abstracting the computation, unnecessary state explorations can be avoided. Computation slicing is an approach for abstracting distributed computations with respect to a given predicate. To detect a predicate in a timely manner during run-time verification, it is important to be able to compute the slice in an incremental manner as and when a new event is generated in the system. In this work, we present several online abstraction algorithms for computing the slice of a distributed computation with respect to regular predicates and its temporal extensions. The family of regular predicates is fairly rich and covers many commonly used predicates for run-time verification. We first present several online algorithms for computing the slice with respect to certain temporal logical regular predicates all of which are centralized. We then present a distributed algorithm for computing the slice with respect to a regular state based predicate; it distributes the work and storage requirements across the system, thus reducing the space and computation complexity per process. We also extend the slicing technique to non-regular predicates by presenting algorithms for computing the slice for two temporal logic operators when the predicate used in the operator is not regular. [ABSTRACT FROM AUTHOR]