computations

Computations are the processes of transforming data into information by applying a sequence of rules to inputs to produce outputs. Computation encompasses both mental calculations and automated processing by mechanical or electronic devices. In computer science, computation is formalized as the execution of algorithms, finite sequences of well-defined steps.

The study of computation has theoretical and practical dimensions. Theoretical foundations include models such as Turing machines, lambda calculus, and finite automata, which capture the essential limits of what can be computed. The Church-Turing thesis posits that any function that can be computed algorithmically can be computed by a Turing machine. Complexity theory analyzes resources such as time and space required to perform computations, leading to classifications such as polynomial or exponential growth and to questions about P versus NP and undecidability.

In practice, computation is performed by computers and other devices, from electrical calculators to modern digital computers and specialized accelerators. Algorithms are implemented in software and executed on hardware, with considerations for precision, reliability, and efficiency. Some computation is performed by non-electronic or natural processes, such as analog computation, neural processing, or physical simulations.

Areas of application include data processing, scientific and engineering simulations, cryptography, optimization, and artificial intelligence. Computations underpin many fields, enabling modeling, analysis, and decision-making. The study of computation also intersects with information theory, mathematics, and philosophy, addressing how information is represented, transformed, and learned.