Circuits Resilient to Short-Circuit Errors

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

SIAM Journal on Computing Pub Date : 2024-07-16 DOI:10.1137/22m1520578

Klim Efremenko, Bernhard Haeupler, Yael Tauman Kalai, Pritish Kamath, Gillat Kol, Nicolas Resch, Raghuvansh R. Saxena

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引用次数: 0

Abstract

SIAM Journal on Computing, Ahead of Print.
Abstract. Given a Boolean circuit [math], we wish to convert it to a circuit [math] that computes the same function as [math], even if some of its gates suffer from adversarial short circuit errors, i.e., their output is replaced by the value of one of their inputs [D. J. Kleitman, F. T. Leighton, and Y. Ma, J. Comput. System Sci., 55 (1997), pp. 385–401]. Can we design such a resilient circuit [math] whose size is roughly comparable to that of [math]? Prior work [T. Kalai, A. B. Lewko, and A. Rao, Formulas resilient to short-circuit errors, in Foundations of Computer Science (FOCS), 2012, pp. 490–499; M. Braverman et al., Optimal short-circuit resilient formulas, in Computational Complexity Conference (CCC), Vol. 137, 2019, pp. 10:1–10:22] gave a positive answer for the special case where [math] is a formula. We study the general case and show that any Boolean circuit [math] of size [math] can be converted to a new circuit [math] of quasi-polynomial size [math] that computes the same function as [math], even if a [math] fraction of the gates on any root-to-leaf path in [math] are short circuited. Moreover, if the original circuit [math] is a formula, the resilient circuit [math] is of near-linear size [math]. The construction of our resilient circuits utilizes the connection between circuits and dag-like communication protocols [A. Razborov, Izvestiya of the RAN, 59 (1995), pp. 201–224; P. Pudlák, On extracting computations from propositional proofs (a survey), in Foundations of Software Technology and Theoretical Computer Science (FSTTCS) Vol. 8, 2010, pp. 30–41; D. Sokolov, Dag-like communication and its applications, in Computer Science Symposium in Russia (CSR), Springer, 2017, pp. 294–307], originally introduced in the context of proof complexity.

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可抵御短路错误的电路

SIAM 计算期刊》，提前印刷。摘要给定一个布尔电路 [math]，我们希望将它转换成一个电路 [math]，即使其中一些门出现对抗性短路错误，即它们的输出被其中一个输入的值所取代，它仍能计算与 [math] 相同的函数 [D. J. Kleitman, F. T. Leighton, and Y. Ma, J. Computing.J. Kleitman, F. T. Leighton, and Y. Ma, J. Comput.系统科学》，55 (1997)，第 385-401 页]。我们能否设计出这样一种弹性电路[math]，其大小与[math]大致相当呢？先前的工作 [T. Kalai, A. B. Lew.Kalai, A. B. Lewko, and A. Rao, Formulas resilient to short-circuit errors, in Foundations of Computer Science (FOCS), 2012, pp.我们研究了一般情况，并证明任何大小为 [math] 的布尔电路 [math] 都能转换成一个准多项式大小为 [math] 的新电路 [math]，即使 [math] 中任何根到叶路径上有 [math] 部分的门被短路，它也能计算与 [math] 相同的函数。此外，如果原始电路[math]是一个公式，弹性电路[math]的大小[math]也接近线性。我们的弹性电路的构造利用了电路与类似达格的通信协议之间的联系 [A. Razborov, Izvests.Razborov, Izvestiya of the RAN, 59 (1995), pp. 201-224; P. Pudlák, On extracting computations from propositional proofs (a survey), in Foundations of Software Technology and Theoretical Computer Science (FSTTCS) Vol. 8, 2010, pp.

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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.