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Truebit is a recent proposal for building smart contracts on top of Ethereum. Truebit allows outsourcing complex computations to untrusted parties, verifying that the computation was done correctly, and paying them for their work. The enforcement and incentives are implemented as a set of Ethereum smart contracts. This is an improvement over current Ethereum, as currently the gas limit means that Ethereum smart contracts can only perform a limited amount of computation.

There are various proposals for sharding, which allow the Ethereum blockchain to scale to a larger number of transactions. They might plausibly allow for increasing the gas limit. So, they could be viewed as an alternative to Truebit.

What advantages and disadvantages does Truebit have over sharding, as a way of allowing smart contracts to perform more computation?

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They solve different problems and can be both used together.

Truebit is about outsourcing heavy computations. For example a simulation may require thousands of hours of computing. You only need in the blockchain the final result and a protocol to ensure the result matches the algorithm output. But the computations are done outside of the blockchain.

Sharding is about not having the whole network validate all transactions. But each transaction still has to be run in at least one node. The amount of computations is limited by how powerfull a node can be. Transaction should be cheaper because nodes do not have to validate all transaction meaning you can process more transactions.

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