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I want to compare the Proof of Stake in Tezos to Proof of Work in Bitcoin. My assumption is that it is far more cheap in complexity to do that in Tezos as the calculation is not involved to the Proof. But there is still some calculation / comparison made. What is the difference in magnitude?

What is the scale of complexity difference and thus the difference of processor time needed? 1 vs N or 1 vs N^2 or something else?

I select the N as variable of loops or iterations and of course N^2 or even 2^N denote kind of exponential difference.

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    Your question does not make sense: Michelson is the smart contract bytecode of Tezos, and you compare it with the mining algorithm of Bitcoin, something that does not exist in Tezos.
    – lefessan
    Commented Mar 11, 2019 at 13:16
  • Michelson is algorithm of Tezos contracts, right? To confirm one contract, how difficult a task it is compared to verifying by counting in Bitcoin? (sorry, the original question was badly formatted)
    – mico
    Commented Mar 11, 2019 at 13:20
  • I know that Bitcoin relies on calculation on confirming contracts and I want to compare the efficiency by computer processor time approximately to the effort on Tezos for the same thing.
    – mico
    Commented Mar 11, 2019 at 13:23
  • Again, Michelson is a language, it is not an algorithm. If you have a particular task to compute in a smart contract, you might want to compare how long it takes to execute, when written in the two different languages. Yet, there are many tasks that you cannot write in Bitcoin’s language, and Tezos is tuned for correctness, not for speed, but I am not aware of any benchmark between smart contract execution engines.
    – lefessan
    Commented Mar 11, 2019 at 13:35
  • Does it make now any sense, more than before? At least I tried more to make understandable what I want to compare and use right terms.
    – mico
    Commented Mar 11, 2019 at 17:27

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I believe you should read a little bit more about the consensus protocol of tezos. For example those links are good

You will see there that Tezos is not reaching consensus by cracking some CPU-hard problem, it's a different mechanism called LPOS (Liquid Proof of Stake)

Also Michelson is the language of smart contracts. By itself it has nothing to do with the consensus protocol itself. Michelson could work exactly the same under a different consensus protocol and LPOS could support another smart contract language that has nothing to do with Michelson.

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