On the optimal space complexity of consensus for anonymous processes

Gelashvili, Rati

doi:10.1007/s00446-018-0331-9

Cited by 7 publications

(6 citation statements)

References 16 publications

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“…The proof of our main result (see Lemma 1) further extends the adversarial framework of [37] to exploit the notion of register covering (originally due to [10]) extended to fault-prone base registers as in [2]. Covering arguments have been successfully applied to proving numerous space lower bound results in the literature (see [6] for a survey) including the recent tight bounds for obstruction-free consensus [20,39], which are at the heart of the space hierarchy of [17].…”

Section: Base Objectmentioning

confidence: 90%

Space Complexity of Fault-Tolerant Register Emulations

Chockler

Spiegelman

2017

Proceedings of the ACM Symposium on Principles of Distributed Computing

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Driven by the rising popularity of cloud storage, the costs associated with implementing reliable storage services from a collection of fault-prone servers have recently become an actively studied question. The well-known ABD result shows that an f -tolerant register can be emulated using a collection of 2f + 1 fault-prone servers each storing a single read-modify-write object type, which is known to be optimal. In this paper we generalize this bound: we investigate the inherent space complexity of emulating reliable multi-writer registers as a fucntion of the type of the base objects exposed by the underlying servers, the number of writers to the emulated register, the number of available servers, and the failure threshold.We establish a sharp separation between registers, and both max-registers (the base object types assumed by ABD) and CAS in terms of the resources (i.e., the number of base objects of the respective types) required to support the emulation; we show that no such separation exists between max-registers and CAS. Our main technical contribution is lower and upper bounds on the resources required in case the underlying base objects are fault-prone read/write registers. We show that the number of required registers is directly proportional to the number of writers and inversely proportional to the number of servers. * Alexander Spiegelman is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship.

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Section: Base Objectmentioning

confidence: 90%

Space Complexity of Fault-Tolerant Register Emulations

Chockler

Spiegelman

2017

Proceedings of the ACM Symposium on Principles of Distributed Computing

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“…For some recent papers and references herein see, e.g. [7,15]. Closer to our paper is [16] where the anonymous asynchronous MWMR fault-tolerant shared-memory model is considered.…”

Section: Mwmrmentioning

confidence: 98%

A characterization of colorless anonymous $t$-resilient task computability

Delporte-Gallet¹,

Fauconnier²,

Rajsbaum³

et al. 2017

Preprint

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A task is a distributed problem for n processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input or output value of another process. Colorless tasks are well studied in the non-anonymous sharedmemory model where each process has a distinct identifier that can be used to access a single-writer/multi-reader shared register. In the anonymous case, where processes have no identifiers and communicate through multiwriter/multi-reader registers, there is a recent topological characterization of the colorless tasks that are solvable when any number of asynchronous processes may crash.In this paper we study the case where at most t processes may crash, where 1 ≤ t < n. We prove that a colorless task is t-resilient solvable non-anonymously if and only if it is t-resilient solvable anonymously. This implies a complete characterization of colorless anonymous t-resilient asynchronous task computability.

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“…As far as we know, O(n) transient space complexity is the best known result. In the shared memory model, a lower bound of Ω(n) registers exists [13], suggesting that the total amount of persistent memory in the system is optimal.…”

Section: Our Contributionmentioning

confidence: 99%

Information Theoretic HotStuff

Abraham¹,

Stern²

2020

Preprint

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is work presents Information eoretic HotStu (IT-HS), a new optimally resilient protocol for solving Byzantine Agreement in partial synchrony with information theoretic security guarantees. In particular, IT-HS does not depend on any PKI or common setup assumptions and is resilient to computationally unbounded adversaries. IT-HS is based on the Primary-Backup view-based paradigm.In IT-HS, in each view, and in each view change, each party sends only a constant number of words to every other party. is yields an O (n 2 ) word and message complexity in each view. In addition, IT-HS requires just O (1) persistent local storage and O (n) transient local storage. Finally, like all Primary-Backup view-based protocols in partial synchrony, a er the system becomes synchronous, all nonfaulty parties decide on a value in the rst view a nonfaulty leader is chosen. Moreover, like PBFT and HotStu , IT-HS is optimistically responsive: with a nonfaulty leader, parties decide as quickly as the network allows them to do so, without regard for the known upper bound on network delay. Our work improves in multiple dimensions upon the information theoretic version of PBFT presented by Miguel Castro, and can be seen as an information theoretic variant of the HotStu paradigm.

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On the optimal space complexity of consensus for anonymous processes

Cited by 7 publications

References 16 publications

Space Complexity of Fault-Tolerant Register Emulations

Space Complexity of Fault-Tolerant Register Emulations

A characterization of colorless anonymous $t$-resilient task computability

Information Theoretic HotStuff

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