The Turing-complete adjective applies in Informatique and logic to a formal Système having the capacity of the machines of Turing.
Thus a Computer programming language is known as Turing-complete if it makes it possible to represent all the calculable functions within the meaning of Turing and Church (notwithstanding the finitude of the memory of the computers). Majority of the usual languages of programming (C, C++, Java,…) are Turing-complete. The fact of being Turing-complete is generally necessary for a generic computer programming language. On the other hand, it is not the case for a language dedicated to the treatment of specific problems.
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