为什么基于扩展的证明失败

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2023-07-25 DOI:10.1137/20m1375851

Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili, Leqi Zhu

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引用次数: 0

摘要

SIAM计算机学报，第52卷，第4期，913-944页，2023年8月。摘要。我们引入了基于扩展的证明，这是一类不可能证明，它包含了价参数。它们被建模为证明者和协议之间的交互。使用基于组合拓扑的证明，已经证明在异步模型中，不可能以无等待的方式确定性地解决[math]进程之间的[math]集协议或[math]进程之间长度为4的周期的近似协议，其中进程使用可以从共享寄存器构造的对象进行通信。然而，基于更简单技术的证明是否可能是未知的。我们证明了在迭代快照模型中，这些不可能的结果不能通过基于扩展的证明得到，因此，基于扩展的证明在功能上是有限的。

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Why Extension-Based Proofs Fail

SIAM Journal on Computing, Volume 52, Issue 4, Page 913-944, August 2023.
Abstract. We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve [math]-set agreement among [math] processes or approximate agreement on a cycle of length 4 among [math] processes in a wait-free manner in asynchronous models where processes communicate using objects that can be constructed from shared registers. However, it was unknown whether proofs based on simpler techniques were possible. We show that these impossibility results cannot be obtained by extension-based proofs in the iterated snapshot model and, hence, extension-based proofs are limited in power.

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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.