Computation refers to the process of performing mathematical operations or processing information according to a defined set of rules or algorithms. It encompasses a wide variety of activities, from simple arithmetic calculations to complex problem-solving tasks performed by computers. Key aspects of computation include: 1. **Algorithms**: These are step-by-step procedures or formulas for solving problems. Algorithms form the basis of computation, guiding how inputs are transformed into outputs.
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A computation applies specified rules to represented information to obtain a result. The rules may operate on exact integers, symbolic expressions or approximate numerical values; the representation determines which operations and errors must be considered.
The Euclidean algorithm computes a greatest common divisor by replacing with until the second entry is zero. For the pairs become , and , yielding six. The identity proves correctness, while decreasing positive remainders prove termination. Computability theory asks whether a suitable algorithm exists; computational complexity asks what resources it requires.