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They can offer improvements in scalability because they don't do any computation by default. Instead, after a transaction they propose the new state to mainnet, or "notarise" the transaction.
With Optimistic rollups, transactions are written to the main Ethereum chain as calldata, optimising them further by reducing the gas cost. As computation is the slow, expensive part of using Ethereum, Optimistic rollups can offer up to x improvements in scalability dependent on the transaction.
This number will increase even more with the introduction of shard chains. This is because there will be more data available in the event that a transaction is disputed. Disputing transactions Optimistic rollups don't actually compute the transaction, so there needs to be a mechanism in place to ensure transactions are legitimate and not fraudulent.
This is where fraud proofs come in. If someone notices a fraudulent transaction, the rollup will execute a fraud-proof and run the transaction's computation, using the available state data.
This means you may have longer wait times for transaction confirmation than a ZK-rollup, because it could be challenged. The gas you need to run the computation of the fraud proof is even reimbursed.
Ben Jones from Optimism describes the bonding system in place: "anyone who might be able to take an action that you would have to prove fraudulent to secure your funds requires that you post a bond. If I don't tell the truth and fraud is proven, this money will be slashed. Not only does some of this money get slashed but some of it will pay for the gas that people spent doing the fraud proof" So you can see the incentives: particpants get penalized for conducting fraud and reimbursed for proving fraud.
Long wait times viteza de pornire dating eth on-chain transaction due to potential fraud challenges. All transaction data is stored on the layer 1 chain, meaning it's secure and decentralized.
Use Optimistic rollups.