Computable

Computable, in the realm of computer science and mathematics, describes a function, problem, or set of data that can be solved or processed by a computational device, typically a computer, through a finite sequence of well-defined instructions or algorithms. A computable function is one where, given any valid input, a corresponding output can be determined through a step-by-step process. This doesn't necessarily mean the solution is easily or efficiently found, just that a computational process exists to arrive at it. The concept is fundamental to understanding the limits of what computers can achieve and the theoretical underpinnings of computation. The notion often deals with 'Turing Computability', a mathematical model of computation used in computer science to test the limits of what computers can achieve in order to classify problems.

Computable meaning with examples

• The travelling salesman problem, finding the shortest route visiting all cities, is a computable problem. While finding an optimal solution can become computationally expensive for a large number of cities, the problem itself can, theoretically, be solved using a computer. Exhaustive search is a computable method.
• A simple arithmetic operation, such as adding two numbers, is inherently computable. A computer can flawlessly perform the addition following a pre-programmed algorithm. The input numbers are processed and a valid result, the sum, is generated. The process is finite and deterministic.
• A function that generates the Fibonacci sequence is also computable, where each number is the sum of the two preceding ones, starting from 0 and 1. With a clear algorithm and appropriate hardware, a computer can calculate any term of the sequence. Recursive algorithms make this computable.
• Many scientific simulations, like weather forecasting or modeling complex physical systems, rely on computable models. Although these models can be incredibly complex and require significant computing power, the calculations involved are, in principle, defined in a computable form, enabling the production of predictive results.