In terms of certifying things with communication, the formal CS studies are done under the name http://en.wikipedia.org/wiki/Interactive_proof_system . In particular, you might be interested in the notion of a http://en.wikipedia.org/wiki/Probabilistically_checkable_proof .
In terms of certifying things with communication, the formal CS studies are done under the name http://en.wikipedia.org/wiki/Interactive_proof_system . In particular, you might be interested in the notion of a http://en.wikipedia.org/wiki/Probabilistically_checkable_proof .