A system that in principle could be able to solve any computation problem.
In order to be called Turing complete, a system has to be able to do what a Turing machine — a theoretical machine developed by mathematician Alan Turing — can do.
Most computer programming languages in use today are Turing complete, but it is not necessary for blockchains to fit this requirement.
An important feature of a Turing-complete language is loops, which allow the programming language to do a set of instructions over and over again.
Bitcoin’s scripting language is not equipped with this. The reason this blockchain is not Turing complete is to prevent spams and network overload.
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