Abstract

It is known that each algorithm is Turing solvable. In the context of function computability, the Church-Turing thesis states that each intuitively computable function is Turing computable. The languages accepted by Turing machines form the recursively enumerable language family L 0 and, according to the Church-Turing thesis, L 0 is also the class of algorithmic computable sets. In spite of its generality, the Turing model can not solve any problem. Recall, for example, that the halting problem is Turing unsolvable: it is algorithmic undecidable if an arbitrary Turing machine will eventually halt when given some specified, but arbitrary, input.

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