{"id":344678,"date":"2017-01-01T16:24:07","date_gmt":"2017-01-02T00:24:07","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=344678"},"modified":"2018-10-16T21:49:43","modified_gmt":"2018-10-17T04:49:43","slug":"formulas-resilient-short-circuit-errors","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/formulas-resilient-short-circuit-errors\/","title":{"rendered":"Formulas Resilient to Short-Circuit Errors"},"content":{"rendered":"
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We show how to efficiently convert any boolean formula F into a boolean formula E that is resilient to short-circuit errors (as introduced by Kleitman et al. [KLM94]). A gate has a short-circuit error when the value it computes is replaced by the value of one of its inputs. We guarantee that E computes the same function as F, as long as at most (1\/10 – e) of the gates on each path from the output to an input have been corrupted in E. The corruptions may be chosen adversarially, and may depend on the formula E and even on the input. We obtain our result by extending the Karchmer-Wigderson connection between formulas and communication protocols to the setting of adversarial error. This enables us to obtain error-resilient formulas from error-resilient communication protocols.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

We show how to efficiently convert any boolean formula F into a boolean formula E that is resilient to short-circuit errors (as introduced by Kleitman et al. [KLM94]). A gate has a short-circuit error when the value it computes is replaced by the value of one of its inputs. 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