Computation is any type of
arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
or non-arithmetic
calculation that follows a well-defined model (e.g., an
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
).
Mechanical or electronic devices (or,
historically
History (derived ) is the systematic study and the documentation of the human activity. The time period of event before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well ...
, people) that perform computations are known as ''
computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These prog ...
s''. An especially well-known discipline of the study of computation is
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
.
Physical process of Computation
Computation can be seen as a purely physical process occurring inside a closed
physical system called a
computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These prog ...
. Examples of such physical systems are
digital computers,
mechanical computers,
quantum computer
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Thoug ...
s,
DNA computers,
molecular computers, microfluidics-based computers,
analog computers, and
wetware computers.
This point of view has been adopted by the
physics of computation
The study of the physics of computation relates to understanding the fundamental physical limits of computers. This field has led to the investigation of how thermodynamics limits information processing, the understanding of chaos and dynamical ...
, a branch of theoretical physics, as well as the field of
natural computing.
An even more radical point of view,
pancomputationalism (inaudible word), is the postulate of
digital physics that argues that the evolution of the universe is itself a computation.
The mapping account
The classic account of computation is found throughout the works of
Hilary Putnam and others.
Peter Godfrey-Smith
Peter Godfrey-Smith (born 1965) is an Australian philosopher of science and writer, who is currently Professor of History and Philosophy of Science at the University of Sydney. He works primarily in philosophy of biology and philosophy of mind, ...
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 and the computation such that the "microphysical states
f the system
F, or f, is the sixth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ef'' (pronounced ), and the plural is ''efs''.
Hist ...
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 be a necessary condition for computation (that is, 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
Digital physics is a speculative idea that the universe can be conceived of as a vast, digital computation device, or as the output of a deterministic or probabilistic computer program. The hypothesis that the universe is a digital computer was ...
, the idea that everything can be said to be computing everything.
The mechanistic account
Gualtiero Piccinini proposes an account of computation based on
mechanical philosophy
The mechanical philosophy is a form of natural philosophy which compares the universe to a large-scale mechanism (i.e. a machine). The mechanical philosophy is associated with the scientific revolution of early modern Europe. One of the first expo ...
. 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" requires that the property can be instantiated by multiple realizers and multiple mechanisms, and that the inputs and outputs of the mechanism also be
multiply realizable. In short, medium-independence allows for the use of physical variables with properties other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that which occurs in the
brain
A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
or in a
quantum computer
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Thoug ...
. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system.
Mathematical models
In the
theory of computation, a diversity of mathematical models of computation has been developed.
Typical mathematical
models of computers are the following:
* State models including
Turing machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer alg ...
,
pushdown automaton,
finite state automaton, and
PRAM
Pram or PRAM may refer to: a bulbous growth on senior canines, varying in size, usually benign and painless. If it bursts, it will ooze pus and blood.
Places
* Pram, Austria, a municipality in the district of Grieskirchen in the Austrian state o ...
* Functional models including
lambda calculus
* Logical models including
logic programming
* Concurrent models including
actor model and
process calculi
Giunti calls the models studied by computation theory ''computational systems,'' and he argues that all of them are mathematical
dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...
s with discrete time and discrete state space. He maintains that a computational system is a complex object which consists of three parts. First, a mathematical dynamical system
with discrete time and discrete state space; second, a computational setup
, which is made up of a theoretical part
, and a real part
; third, an interpretation
, which links the dynamical system
with the setup
.
See also
*
Computationalism
*
Real computation
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible ...
*
Reversible computation
Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary co ...
*
Hypercomputation
*
Lateral computing
*
Computational problem
*
Multiple realizability
*
Limits of computation
References
{{Reflist
Theoretical computer science
Computability theory