 
Summary: Formulas Resilient to ShortCircuit Errors
Yael Kalai
Allison Lewko
Anup Rao
Abstract
We show how to efficiently convert any boolean formula F into a boolean formula E that is
resilient to shortcircuit errors (as introduced by Kleitman et al. [KLM94]). A gate g has a
shortcircuit 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 KarchmerWigderson connection between formulas and communication
protocols to the setting of adversarial error. This enables us to obtain errorresilient formulas
from errorresilient communication protocols.
Microsoft Research, yael@microsoft.com.
The University of Texas at Austin, alewko@cs.utexas.edu. Supported by a Microsoft Research PhD Fellowship.
University of Washington, anuprao@cs.washington.edu. Supported by the National Science Foundation under
