TURING COMPUTABLE FUNCTION Meaning and
Definition
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A Turing computable function, also known as a computable function or Turing machine computable function, refers to a mathematical function that can be computed or performed by a Turing machine. A Turing machine is a hypothetical device, created by the mathematician Alan Turing in the 1930s, that is capable of solving any problem that can be solved by a mechanical method.
Turing computable functions are a fundamental concept in computer science and computational theory, as they represent the class of functions that can be computed by a Turing machine. These functions are characterized by their ability to take some input and produce an output based on a specific set of rules or algorithms.
The computational power of Turing machines lies in their ability to manipulate symbols on an unlimited length tape, according to the instructions or program provided to them. Turing computable functions can perform various operations such as addition, subtraction, multiplication, and division, as well as more complex tasks like sorting, searching, and decision making.
In simpler terms, a Turing computable function is a function that can be calculated step-by-step by a theoretical machine called a Turing machine. These functions have a well-defined process or algorithm that can be followed to obtain the desired output based on a given input. The concept of Turing computable functions is crucial for understanding the theoretical limits and capabilities of computing machines and is a cornerstone of the field of computer science.
