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High Quality Content by WIKIPEDIA articles! A computational system that can compute every Turing-computable function is called Turing-complete (or Turing-powerful). Alternatively, such a system is one that can simulate a universal Turing machine.A Turing-complete system is called Turing-equivalent if every function it can compute is also Turing-computable; i.e., it computes precisely the same class of functions as do Turing machines. Alternatively, a Turing-equivalent system is one that can simulate, and be simulated by, a universal Turing machine. (All known Turing-complete systems are Turing-equivalent, which adds support to the Church-Turing thesis.)