可判定性和可计算性之间的区别

可计算性和可判定性都告诉我们是否存在针对特定问题或函数的算法，在解决特定问题时，确定问题是否可解决对我们来说非常重要，这在两个方面都很重要效率和执行力。因此，确定可计算性和可判定性对于确定问题是否可以在有限的时间内解决非常重要。尽管它们听起来很相似，但它们之间存在细微的差异。在本文中，我们将简要讨论可计算性和可判定性之间的区别。

可计算性：

一个问题的可计算性可以定义为它是否可以无限地解决。它与是否存在解决问题的算法的想法有关。

因此，我们可以将可计算性定义为算法上可计算的问题或函数。换句话说，我们可以通过图灵机计算的能力来定义问题或函数的可计算性，对于给定的输入，如果图灵机停止并产生输出，我们可以将其声明为可计算的。

可判定性：

可判定性是一个更简单的概念，我们试图找出给定问题是否存在将在给定域内停止的算法或图灵机。

可判定问题的输出是“是”或“否”。可判定性是一个广义的概念，我们试图找出是否有一个图灵机可以接受并停止域上定义的问题的每个输入。

可判定性和可计算性之间的区别：

S. No.	Computability	Decidability
1.	Computability talks about if the problem can be calculated algorithmically or by a Turing machine.	Decidability talks about if there exists an algorithm to solve a problem or if the Turing machine halts.
2.	If a function or a problem is computable it will take input on the tape of the Turing machine and output on the same tape of the Turing machine.	The output to the decidable problem is either YES or NO.
3.	If the given set is computable it is also decidable.	However decidable sets are not always computable.
4.	Computability is required to decide if the problem is solvable.	Decidability is required to decide if the problem is computable.
5.	Computability is dependent or defined on a particular domain as well as a range.	Decidability is solely dependent or defined on a particular domain.
6.	Computability of a problem/function is a bit critical to apply.	Decidability of a problem/function is much simpler to apply.
7.	Computability is a characteristic concept where we try to find out if we are able to compute every input of a particular problem.	Decidability is a generalized concept where we try to find out if there is the Turing machine that accepts and halts for every input of the problem defined on the domain.
8.	Computability determines the solvability of a problem in finite time.	Decidability determines after certain steps of an algorithm if the answer can be achieved.