Computation is any type of calculation that follows a well-defined model understood and expressed as, for example, an algorithm.
- Physical phenomenon
- The mapping account
- The semantic account
- The mechanistic account
- Mathematical models
The study of computation is paramount to the discipline of computer science.
A computation can be seen as a purely physical phenomenon occurring inside a closed physical system called a computer. Examples of such physical systems include digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers or wetware computers. This point of view is the one adopted by the branch of theoretical physics called the physics of computation as well as the field of natural computing.
An even more radical point of view is the postulate of digital physics that the evolution of the universe itself is a computation - pancomputationalism.
The mapping account
A classic account of computation is found throughout the works of Hilary Putnam and others. Peter Godfrey-Smith has dubbed this the “simple mapping account.” Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system to the computation such that the “microphysical states [of the system] mirror the state transitions between the computational states.”
The semantic account
Philosophers such as Jerry Fodor have suggested various accounts of computation with the restriction that semantic content is a necessary condition for computation (that is, that what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of the mapping account of pancomputationalism, or the idea that everything can be said to be computing everything.
The mechanistic account
Gualtiero Piccinini proposes an account of computation based in mechanical philosophy. It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or “the manipulation (by a functional mechanism) of a medium-independent vehicle according to a rule.” Medium-independence allows for the use of physical variables with traits other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that occurs in the brain or in a quantum computer. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system.
In the theory of computation, a diversity of mathematical models of computers have been developed. Typical mathematical models of computers are the following: