Computation is any type of
arithmetic 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 ''
computers''. 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 practical disciplines (includi ...
.
Physical process of Computation
Computation can be seen as a purely physical process occurring inside a closed
physical system called a
computer. Examples of such physical systems are
digital 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 program ...
s,
mechanical computer
A mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment out ...
s,
quantum computers,
DNA computer
DNA computing is an emerging branch of unconventional computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional electronic computing. Research and development in this area concerns theory, experiments, a ...
s,
molecular computer
DNA computing is an emerging branch of unconventional computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional electronic computing. Research and development in this area concerns theory, experiments, a ...
s, microfluidics-based computers,
analog computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...
s, and
wetware computer
A wetware computer is an organic computer (which can also be known as an artificial organic brain or a neurocomputer) composed of organic material " wetware" such as "living" neurons. Wetware computers composed of neurons are different than conve ...
s.
This point of view has been adopted by the
physics of computation, a branch of theoretical physics, as well as the field of
natural computing
Natural computing,G.Rozenberg, T.Back, J.Kok, Editors, Handbook of Natural Computing, Springer Verlag, 2012A.Brabazon, M.O'Neill, S.McGarraghyNatural Computing Algorithms Springer Verlag, 2015 also called natural computation, is a terminology intro ...
.
An even more radical point of view,
pancomputationalism (inaudible word), is the postulate of
digital physics
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 p ...
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 systemmirror the state transitions between the computational states."
The semantic account
Philosophers such as
Jerry Fodor
Jerry Alan Fodor (; April 22, 1935 – November 29, 2017) was an American philosopher and the author of many crucial works in the fields of philosophy of mind and cognitive science. His writings in these fields laid the groundwork for the modul ...
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
Gualtiero Piccinini (born 1970) is an Italian–American philosopher known for his work on the nature of mind and computation as well as on how to integrate psychology and neuroscience. He is Curators' Distinguished Professor in the Philosophy De ...
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 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 vision. It is the most complex organ in a ve ...
or in a
quantum computer. 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
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how algorithmic efficiency, efficiently they can be solved or t ...
, 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 algori ...
,
pushdown automaton
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is
a type of automaton that employs a stack.
Pushdown automata are used in theories about what can be computed by machines. They are more capab ...
,
finite state automaton
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...
, and
PRAM
* Functional models including
lambda calculus
* Logical models including
logic programming
Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...
* Concurrent models including
actor model and
process calculi
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and ...
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 in ...
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
In philosophy of mind, the computational theory of mind (CTM), also known as computationalism, is a family of views that hold that the human mind is an information processing system and that cognition and consciousness together are a form of c ...
*
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 possibl ...
*
Reversible computation
*
Hypercomputation
Hypercomputation or super-Turing computation refers to models of computation that can provide outputs that are not Turing-computable. Super-Turing computing, introduced at the early 1990's by Hava Siegelmann, refers to such neurological inspired, b ...
*
Lateral computing
*
Computational problem
In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring
:"Given a positive integer ''n'', find a nontrivial prime factor of ''n''."
is a computational probl ...
*
Multiple realizability
Multiple realizability, in the philosophy of mind, is the thesis that the same mental property, state, or event can be implemented by different physical properties, states, or events. Philosophers of mind have used multiple realizability to argue ...
*
Limits of computation
The limits of computation are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energ ...
References
{{Reflist
Theoretical computer science
Computability theory