Quasi-Linearizability is Undecidable

Wang, Chao; Lv, Yi; Liu, Gaoang; Wu, Peng

doi:10.1007/978-3-319-26529-2_20

Cited by 3 publications

(6 citation statements)

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“…There are already several known results pub-lished on the decidability of linearizability and its relaxed variants [9-11, 14, 15]. Specially in a preceding work [11], we proved that quasi-linearizability is undecidable for a bounded number of processes.…”

Section: Introductionmentioning

confidence: 54%

“…In a preceding work [11] we have proved that it is undecidable whether a concurrent data structure is quasi-linearizable with respect to a regular sequential specification for a finite number of processes (even so for only one process), as shown by the following lemma.…”

Section: Definition and Decidability Of Quasi-linearizabilitymentioning

confidence: 96%

“…Lemma 2 (Undecidability of quasi-linearizability [11]). Given a concurrent data structure L, a quasilinearizabilization factor Q and a regular sequential specification Spec, the problem of whether L is Q-quasi-linearizable with respect to Spec for n processes is undecidable.…”

Section: Definition and Decidability Of Quasi-linearizabilitymentioning

confidence: 99%

“…Since linearizability can be regarded as a special case of quasi-linearizability, klinearizability and regular-relaxed linearizability, it is obvious that quasi-linearizability, k-linearizability and regular-relaxed linearizability are also undecidable for an unbounded number of processes. In our previous work [11], we have proved that quasi-linearizability is also undecidable for a bounded number of processes. But the decidability problems of k-linearizablity and regular-relaxed linearizability remain open for a bounded number of processes.…”

Section: Introductionmentioning

confidence: 97%

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Decidability of linearizabilities for relaxed data structures

Wang

2017

Sci. China Inf. Sci.

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Many recent implementations of concurrent data structures relaxed their linearizability requirements for better performance and scalability. Quasi-linearizability, k-linearizability and regular-relaxed linearizability are three quantitative relaxation variants of linearizability that have been proposed as correctness conditions of relaxed data structures, yet preserving the intuition of linearizability. Quasi-linearizability has been proved undecidable. In this paper, we first show that k-linearizability is undecidable for a bounded number of processes, by reducing quasi-linearizability into it. We then show that regular-relaxed linearizability is decidable for a bounded number of processes. We also find that the number of the states of a relaxed specification is exponential to the number of the states of the underlying specification automaton (representing its relaxation strategy), and polynomial to the number of the states of the underlying quantitative sequential specification and the number of operations.

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Section: Introductionmentioning

confidence: 54%

Section: Definition and Decidability Of Quasi-linearizabilitymentioning

confidence: 96%

Section: Definition and Decidability Of Quasi-linearizabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Decidability of linearizabilities for relaxed data structures

Wang

2017

Sci. China Inf. Sci.

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“…The same conclusion holds for systems with only four objects. Wang et al [22] studied the model checking problem of quasi-linearizability and proved that it is undecidable. For consistency criteria weaker than sequential consistency, eventual consistency has been shown to be decidable [12], and causal consistency was proved to be undecidable [19] in general.…”

Section: Undecidability Of Verifying Weak Consistencymentioning

confidence: 99%

The Complexity of Weak Consistency

Liu

2018

Frontiers in Algorithmics

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Weak consistency is a memory model that is frequently considered for shared memory systems. Its most distinguishable feature lies in a category of operations in two types: data operations and synchronization operations. For highly parallel shared memory systems, this model offers greater performance potential than strong models such as sequential consistency by permitting unconstrained optimization on updates propagation before synchronization is invoked. It captures the intuition that delaying updates produced by data operations before triggering a synchronization operation does not typically affect the program correctness. To formalize the connection between concrete executions and the corresponding specification, we propose in this work a new approach to define weak consistency. This formalization, defined in terms of distributed histories abstracted from concrete executions, provides an additional perception of the concept and facilitates automatic analysis of system behaviors. We then investigate the problems on verifying whether implementations have correctly implemented weak consistency. Specifically, we consider two problems: (1) the testing problem that checks whether one single execution is weakly consistent, a critical problem for designing efficient testing and bug hunting algorithms, and (2) the model checking problem that determines whether all executions of an implementation are weakly consistent. We show that the testing problem is NP-complete, even for finite processes and short programs. The model checking problem is proven to be undecidable.

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Decomposable Relaxation for Concurrent Data Structures

Wang

2017

SOFSEM 2017: Theory and Practice of Computer Science

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Quasi-Linearizability is Undecidable

Cited by 3 publications

References 10 publications

Decidability of linearizabilities for relaxed data structures

Decidability of linearizabilities for relaxed data structures

The Complexity of Weak Consistency

Decomposable Relaxation for Concurrent Data Structures

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