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Although the halting problem is not computable, it is possible to simulate program execution and produce an infinite list of the programs that do halt. Thus the halting problem is an example of a recursively enumerable set, which is a set that can be enumerated by a Turing machine (other terms for recursively enumerable include computably enumerable and semidecidable). Equivalently, a set is recursively enumerable if and only if it is the range of some computable function.  The recursively enumerable sets, although not decidable in general, have been studied in detail in recursion theory.

Although the halting problem is not computable, it is possible to simulate program execution and produce an infinite list of the programs that do halt. Thus the halting problem is an example of a recursively enumerable set, which is a set that can be enumerated by a Turing machine (other terms for recursively enumerable include computably enumerable and semidecidable). Equivalently, a set is recursively enumerable if and only if it is the range of some computable function.  The recursively enumerable sets, although not decidable in general, have been studied in detail in recursion theory.

虽然停机问题是不可计算的，但是可以模拟程序执行，并产生一个做停机的程序的无限列表。因此，停止问题就是一个递归可枚举集合的例子，它是一个可以由图灵机枚举的集合(其他可递归枚举的术语包括可计算枚举和半枚举)。等价地，一个集合是递归可枚举的当且仅当它是某个可计算函数的范围。递归可枚举集，尽管一般来说不是可判定的，已经在《可计算性理论作了详细的研究。

虽然停机问题是不可计算的，但是可以模拟程序执行并生成一个无限的程序列表来做停机。因此，停止问题就是一个'''<font color="#ff8000">递归可枚举集合 recursively enumerable set</font>'''的例子，它是图灵机可以枚举的集合(递归枚举的其他术语包括可计算枚举和半可计数)。等价地，集合是递归可枚举的当且仅当它是某些可计算函数的范围。递归可枚举集合虽然在一般情况下是不可判定的，但在递归理论中得到了详细的研究。

==Areas of research==

==Areas of research==