TY - GEN

T1 - Circuits resilient to short-circuit errors.

AU - Efremenko, Klim

AU - Haeupler, Bernhard

AU - Kalai, Yael Tauman

AU - Kamath, Pritish

AU - Kol, Gillat

AU - Resch, Nicolas

AU - Saxena, Raghuvansh R.

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2022/6/10

Y1 - 2022/6/10

N2 - Given a Boolean circuit C, we wish to convert it to a circuit C that computes the same function as C 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. Can we design such a resilient circuit C whose size is roughly comparable to that of C? Prior work gave a positive answer for the special case where C is a formula. We study the general case and show that any Boolean circuit C of size s can be converted to a new circuit C′ of quasi-polynomial size sO(logs) that computes the same function as C even if a 1/51 fraction of the gates on any root-to-leaf path in C are short circuited. Moreover, if the original circuit C is a formula, the resilient circuit C is of near-linear size s1+є. The construction of our resilient circuits utilizes the connection between circuits and DAG-like communication protocols, originally introduced in the context of proof complexity.

AB - Given a Boolean circuit C, we wish to convert it to a circuit C that computes the same function as C 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. Can we design such a resilient circuit C whose size is roughly comparable to that of C? Prior work gave a positive answer for the special case where C is a formula. We study the general case and show that any Boolean circuit C of size s can be converted to a new circuit C′ of quasi-polynomial size sO(logs) that computes the same function as C even if a 1/51 fraction of the gates on any root-to-leaf path in C are short circuited. Moreover, if the original circuit C is a formula, the resilient circuit C is of near-linear size s1+є. The construction of our resilient circuits utilizes the connection between circuits and DAG-like communication protocols, originally introduced in the context of proof complexity.

KW - Error Resilient Computation

KW - Short Circuit Errors

KW - Circuit complexity

UR - http://www.scopus.com/inward/record.url?scp=85132689174&partnerID=8YFLogxK

U2 - 10.1145/3519935.3520007

DO - 10.1145/3519935.3520007

M3 - Conference contribution

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 582

EP - 594

BT - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing June 2022

A2 - Leonardi, Stefano

A2 - Gupta, Anupam

PB - Association for Computing Machinery

T2 - 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022

Y2 - 20 June 2022 through 24 June 2022

ER -