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|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.
|Efremenko, Klim, Haeupler, Bernhard, Kalai, Yael Tauman, Kamath, Pritish, Kol, Gillat, Resch, Nicolas and Saxena, Raghuvansh R. "Circuits resilient to short-circuit errors." Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022): 582-594. doi:10.1145/3519935.3520007
|582 - 594
|Type of Material:
|Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
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