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...which each sequence contains at most two memory operations and each variable occurs in at most two write operations, is NP-complete. Proof. We use a reduction from the 3-Satisfiability (3SAT) problem =-=[13]-=-. Consider a 3SAT instance F with n variables, v1,...,vn,andmclauses, C1,...,Cm.Weuse the notation (vi,S(vi)) to represent either the variable vi (when S(vi) =T) or its complement vi (when S(vi)=F) in...

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...duction. Shared-memory multiprocessors typically promise application and system programmers some high-level view of the memory system. High-level correctness conditions such as sequential consistency =-=[26]-=- provide a conceptually simple framework for programming parallel machines. In a sequentially consistent memory, each execution is indistinguishable (by the processors) from an execution of a (very fa...

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...ishable from an execution of a serial memory, in which each read or write occurs at a distinct point in time between when it is issued by the processor and when the system acknowledges its completion =-=[22]-=-. We define the problem verifying linearizability of shared-memory executions (VL) and show that the additional restrictions imposed by linearizability beyond that of sequential consistency are quite ...

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...arge shared-memory system. Third, certain implementations used in practice provide only an approximation to sequential consistency, e.g., processor consistency, as a tradeoff for improved performance =-=[16]-=-. Fourth, shared-memory multiprocessors may support release consistency [16, 21], which provides a sequentially consistent memory (only) for programs that are free of data races. (A data race occurs w...

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...ondition for multiprocessor memory systems. A memory system promising sequential consistency may fail to provide it for a number of reasons. First, high-performance shared-memory multiprocessors (cf. =-=[5, 7, 12, 27]-=-) employ a variety of techniques to improve their memory system performance (e.g., buffering, pipelining, caching, multiple paths to memory, parallel access to memory banks); these serve to distance t...

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...ondition for multiprocessor memory systems. A memory system promising sequential consistency may fail to provide it for a number of reasons. First, high-performance shared-memory multiprocessors (cf. =-=[5, 7, 12, 27]-=-) employ a variety of techniques to improve their memory system performance (e.g., buffering, pipelining, caching, multiple paths to memory, parallel access to memory banks); these serve to distance t...

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...ess conditions other than linearizability and sequential consistency can be considered. A number of correctness conditions from the domain of database transactions have been previously studied (e.g., =-=[6, 25, 30]-=-). It would be interesting to develop a general theory encompassing a wide range of correctness conditions so that tradeoffs between the generality of a correctness condition and its complexity may be...

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...he references therein), work on computing with faulty shared memories [4], work on de1210 P. B. GIBBONS AND E. KORACH termining minimal ordering constraints needed to preserve sequential consistency =-=[33]-=-, and work on comparing implementations of sequential consistency versus linearizability (e.g., [8]). However, none of this work addresses the general testing questions considered in this paper. 1.1. ...

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...y or a weaker correctness condition [11], work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions =-=[31]-=-, work on detecting data races (e.g., [2, 23, 28, 29]), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on te...

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...ondition for multiprocessor memory systems. A memory system promising sequential consistency may fail to provide it for a number of reasons. First, high-performance shared-memory multiprocessors (cf. =-=[5, 7, 12, 27]-=-) employ a variety of techniques to improve their memory system performance (e.g., buffering, pipelining, caching, multiple paths to memory, parallel access to memory banks); these serve to distance t...

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... help test whether the memory system is providing sequential consistency or a weaker correctness condition [11], work on detecting violations of sequential consistency within the memory system itself =-=[14, 15]-=-, work on testing the serializability of database transactions [31], work on detecting data races (e.g., [2, 23, 28, 29]), work on proving that weak memory systems provide sequential consistency for p...

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...BONS AND E. KORACH termining minimal ordering constraints needed to preserve sequential consistency [33], and work on comparing implementations of sequential consistency versus linearizability (e.g., =-=[8]-=-). However, none of this work addresses the general testing questions considered in this paper. 1.1. The testing problems. During an execution of a parallel program on a given multiprocessor, processo...

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...es (e.g., [2, 23, 28, 29]), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories =-=[9]-=-, work on algorithms for testing data structures on uniprocessors (e.g., [10]), work on verifying specific properties of cache-coherence protocols (e.g., [32] and the references therein), work on comp...

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...problems. Other related previous work includes work on devising a suite of simple programs to help test whether the memory system is providing sequential consistency or a weaker correctness condition =-=[11]-=-, work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions [31], work on detecting data races (e.g....

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...rom an execution of a (very fast) serial memory in which only one read or write occurs at a time, in an order consistent with the respective sequences of reads and writes at the individual processors =-=[26, 3]-=-. Sequential consistency is the most widely used correctness condition for multiprocessor memory systems. A memory system promising sequential consistency may fail to provide it for a number of reason...

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...work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions [31], work on detecting data races (e.g., =-=[2, 23, 28, 29]-=-), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories [9], work on algorithms f...

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...work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions [31], work on detecting data races (e.g., =-=[2, 23, 28, 29]-=-), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories [9], work on algorithms f...

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...ondition for multiprocessor memory systems. A memory system promising sequential consistency may fail to provide it for a number of reasons. First, high-performance shared-memory multiprocessors (cf. =-=[5, 7, 12, 27]-=-) employ a variety of techniques to improve their memory system performance (e.g., buffering, pipelining, caching, multiple paths to memory, parallel access to memory banks); these serve to distance t...

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...tabase transactions [31], work on detecting data races (e.g., [2, 23, 28, 29]), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., =-=[1, 20, 21]-=-), work on testing uniprocessor memories [9], work on algorithms for testing data structures on uniprocessors (e.g., [10]), work on verifying specific properties of cache-coherence protocols (e.g., [3...

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...rovide only an approximation to sequential consistency, e.g., processor consistency, as a tradeoff for improved performance [16]. Fourth, shared-memory multiprocessors may support release consistency =-=[16, 21]-=-, which provides a sequentially consistent memory (only) for programs that are free of data races. (A data race occurs when two or more processors access the same location, with at least one writing, ...

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...er, we consider read, write, and read–modify–write operations. This is extended in [17, 19], where we also consider the load-reserved (a.k.a. load-linked, loadlocked) and store-conditional operations =-=[24]-=- appearing in many recent architectures. More generally, one can consider testing shared memories that support various data structures, such as priority queues. Finally, correctness conditions other t...

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...work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions [31], work on detecting data races (e.g., =-=[2, 23, 28, 29]-=-), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories [9], work on algorithms f...

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... help test whether the memory system is providing sequential consistency or a weaker correctness condition [11], work on detecting violations of sequential consistency within the memory system itself =-=[14, 15]-=-, work on testing the serializability of database transactions [31], work on detecting data races (e.g., [2, 23, 28, 29]), work on proving that weak memory systems provide sequential consistency for p...

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...1]), work on testing uniprocessor memories [9], work on algorithms for testing data structures on uniprocessors (e.g., [10]), work on verifying specific properties of cache-coherence protocols (e.g., =-=[32]-=- and the references therein), work on computing with faulty shared memories [4], work on de1210 P. B. GIBBONS AND E. KORACH termining minimal ordering constraints needed to preserve sequential consis...

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...work on detecting violations of sequential consistency within the memory system itself [14, 15], work on testing the serializability of database transactions [31], work on detecting data races (e.g., =-=[2, 23, 28, 29]-=-), work on proving that weak memory systems provide sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories [9], work on algorithms f...

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...ting such memories. In particular, we present O(n log n)-time algorithms for several variants of the VL problem whose corresponding VSC variants are NP-complete. In an independent work, Wing and Gong =-=[34]-=- defined and studied the problem of testing and verifying linearizability for arbitrary shared data structures (e.g., a FIFO queue with push and pop operations). They developed a simulation environmen...

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...ata structures on uniprocessors (e.g., [10]), work on verifying specific properties of cache-coherence protocols (e.g., [32] and the references therein), work on computing with faulty shared memories =-=[4]-=-, work on de1210 P. B. GIBBONS AND E. KORACH termining minimal ordering constraints needed to preserve sequential consistency [33], and work on comparing implementations of sequential consistency ver...

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... sequential consistency for programs that are free of data races (e.g., [1, 20, 21]), work on testing uniprocessor memories [9], work on algorithms for testing data structures on uniprocessors (e.g., =-=[10]-=-), work on verifying specific properties of cache-coherence protocols (e.g., [32] and the references therein), work on computing with faulty shared memories [4], work on de1210 P. B. GIBBONS AND E. K...

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...ess conditions other than linearizability and sequential consistency can be considered. A number of correctness conditions from the domain of database transactions have been previously studied (e.g., =-=[6, 25, 30]-=-). It would be interesting to develop a general theory encompassing a wide range of correctness conditions so that tradeoffs between the generality of a correctness condition and its complexity may be...

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...mic results can be extended to handle atomic read–modify–write operations, with no asymptotic penalty. Our algorithms have small constants and hence are suitable for testing real shared memories (see =-=[17, 19]-=- for implementation details). Since this is the first paper to study these problems systematically, a number of our NP-completeness results are obtained using somewhat standard techniques. For more in...

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...fically, a read-mapping, write-order, read&write only, and conflict-order. It also presents our extensions to handle atomic read-modify-write operations. Preliminary versions of this work appeared in =-=[18, 19]-=-. 2. Verifying sequential consistency. We begin this section with a proof that the VSC problem is NP-complete, even with only two operations per processor (section 2.1). Then the VSC problem is shown ...

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...ess conditions other than linearizability and sequential consistency can be considered. A number of correctness conditions from the domain of database transactions have been previously studied (e.g., =-=[6, 25, 30]-=-). It would be interesting to develop a general theory encompassing a wide range of correctness conditions so that tradeoffs between the generality of a correctness condition and its complexity may be...

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...mic results can be extended to handle atomic read–modify–write operations, with no asymptotic penalty. Our algorithms have small constants and hence are suitable for testing real shared memories (see =-=[17, 19]-=- for implementation details). Since this is the first paper to study these problems systematically, a number of our NP-completeness results are obtained using somewhat standard techniques. For more in...