Summary: Formulas Resilient to Short-Circuit Errors
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 g has a
short-circuit error when the value it computes is replaced by the value of one of g's inputs.
We guarantee that E computes the same function as F, as long as at most (1/10 - ) 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.
Microsoft Research, firstname.lastname@example.org.
The University of Texas at Austin, email@example.com. Supported by a Microsoft Research PhD Fellowship.
University of Washington, firstname.lastname@example.org. Supported by the National Science Foundation under