  We consider fault-tolerant boolean formulas in which the output of a faulty
gate is short-circuited to one of the gate's inputs. A recent result by Kalai
et al. (FOCS 2012) converts any boolean formula into a resilient formula of
polynomial size that works correctly if less than a fraction $1/6$ of the gates
(on every input-to-output path) are faulty. We improve the result of Kalai et
al., and show how to efficiently fortify any boolean formula against a fraction
$1/5$ of short-circuit gates per path, with only a polynomial blowup in size.
We additionally show that it is impossible to obtain formulas with higher
resilience and sub-exponential growth in size.
  Towards our results, we consider interactive coding schemes when noiseless
feedback is present; these produce resilient boolean formulas via a
Karchmer-Wigderson relation. We develop a coding scheme that resists up to a
fraction $1/5$ of corrupted transmissions in each direction of the interactive
channel. We further show that such a level of noise is maximal for coding
schemes with sub-exponential blowup in communication. Our coding scheme takes a
surprising inspiration from Blockchain technology.
