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It's just a database, but it's distributed, with integrity maintained through public keys

Coins, inventory, cars, loans, art, crypto kitties, sensor logs, records.. anything you'd put in a database, you could instead put into the distributed ledger and forget about it (at a price, the amount of data has to be very small but you can also buy hosting separately). Others can then have assurances about the integrity of that ledger without having to trust you either

The cherry on top is being able to write transform functions (ie programs) that all of the nodes simultaneously run so the ledger state can intelligently change based on conditions

Thanks, but what you're describing is already possible with traditional technologies.

What specific advantage does the blockchain provide here, given decentralisation is less efficient than the centralised cloud solutions already available from providers like AWS?

Assuming you mean public blockchains, the main advantage is censorship resistance (you cannot have an administrator delete entries or restrict access).

But where is this useful? I can already set up databases with restricted access to certain users.

In what situations am I going to want to create a database in which not even I under any circumstances can delete things or change access rights?

You are thinking of operations within a centrally controlled, trusted entity. This is useful for things that happen between entities that don't necessarily trust each other and don't have control of each other's data. Data interoperability, dealing with sketchy vendors, and chain of ownership through many companies, nations, or even departments within large organizations are huge problems that an insane amount of money is thrown at. There is a lot of value in a database of facts that no-one controls and everyone can trust.

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