All these operations need access to the "external world" or are very expensive.

How does an Ethereum Smart Contract

TrueBit - the Verification Game

Cooperation with Loi Luu (U. Singapore) and Jason Teutsch (U. Alabama), based on "How to verify computation with a rational network".

Interactive verification mechanism proposed by Canetti, Riva, Rothblum: "Practical delegation of computation using multiple servers", 2011

Make this work on a blockchain by adding economic incentives.