The general purpose analog computer (GPAC) is a mathematical model of

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 c ...

s first introduced in 1941 by

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-o ...

. This model consists of circuits where several basic units are interconnected in order to

compute Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, e ...

some

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

. The GPAC can be implemented in practice through the use of mechanical devices or

analog electronics Analogue electronics ( en-US, analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relati ...

. Although analog computers have fallen almost into oblivion due to emergence of the

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 pro ...

, the GPAC has recently been studied as a way to provide evidence for the physical Church–Turing thesis. This is because the GPAC is also known to model a large class of

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

s defined with

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...

s, which appear frequently in the context of

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. In particular it was shown in 2007 that (a deterministic variant of) the GPAC is equivalent, in

computability Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is close ...

terms, to

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 ...

s, thereby proving the physical Church–Turing thesis for the class of systems modelled by the GPAC. This was recently strengthened to

polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

equivalence.

Definition and history

The General Purpose Analog Computer was originally introduced by

. This model came as a result of his work on

Vannevar Bush Vannevar Bush ( ; March 11, 1890 – June 28, 1974) was an American engineer, inventor and science administrator, who during World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almost all wartime ...

differential analyzer The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operati ...

, an early

. Shannon defined the GPAC as an analog circuit consisting of five types of units: adders (which add their inputs), multipliers (which multiply their inputs),

integrator An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an importan ...

s, constant units (which always output the value 1), and constant multipliers (which always multiply their input by a fixed constant ''k''). More recently, and for simplicity, the GPAC has instead been defined using the equivalent four types of units: adders, multipliers, integrators and real constant units (which always output the value ''k'', for some fixed

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

''k''). In his original paper, Shannon presented a result which stated that functions computable by the GPAC are those functions which are differentially algebraic.

References

{{reflist

External links

The Analog Thing
An open-source analog computer Analog computers

Definition and history

See also

References

External links