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As I understand: each epoch a winner-miner broadcasts a new block to the tail of the block-chain, which contains the block's transaction list, with n transactions executed by the block and some other information. This is well explained on Ethereum's white paper:

After a new block is selected, what will be the other miner's and full-nodes' role should will be, in order to approve/accept the new block?

[Q] Does all the miners and/or full-client nodes require to re-execute the each transaction in order to approve/accept the new block? If yes:

Would that consume additional computational power to re-execute each transaction by each node over and over again? and is there any alternative solution to over-come this additional computation.

If no: Is there any other approval mechanism without doing re-execution of the approved transactions by the full-nodes?

Thank you for your valuable time and help.

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Yes, each node should validate each transaction, including running smart contract code. Yes, this takes compute power on each node.

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  • This is very inefficient @smarx
    – alper
    Commented Dec 22, 2017 at 16:11
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    In some sense, I agree, but this "inefficiency" serves a vital function. Blockchain technology trades off efficiency for "trustless" computation. Because all the nodes repeat the computation, they can reject invalid transactions. Also, keep in mind that computers are fast, and there aren't that many transactions per second. (My laptop has no trouble keeping up with all the activity in Ethereum right now.) In the future, as there are more transactions per second, other solutions such as sharding will help reduce the per-node work.
    – user19510
    Commented Dec 22, 2017 at 16:17
  • Only disadvantage is heavy limitation on EVM-side: storage(read/write) is pretty expensive. Also since ethereum price increases in $, GAS price keep increases and not constant. Which forces us to implement compact code as possible, which cannot do much. @smarx
    – alper
    Commented Dec 22, 2017 at 16:25

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