General purpose analog computer

<p>The general purpose analog computer (GPAC) is a mathematical model of <a href="/facts/Analog_computer/3NhYoCML">analog computers</a> first introduced in 1941 by <a href="/facts/Claude_Shannon/EremsCws">Claude Shannon</a>. This model consists of circuits where several basic units are interconnected in order to <a href="/facts/Computation/qLsELosq">compute</a> some <a href="/facts/Function_(mathematics)/CdReEKCh">function</a>. The GPAC can be implemented in practice through the use of <a href="/facts/Differential_analyser/lgA1m3VS">mechanical devices</a> or <a href="/facts/Analogue_electronics/Bnlnfwwv">analog electronics</a>. Although analog computers have fallen almost into oblivion due to emergence of the <a href="/facts/Computer/SQe1aK05">digital computer</a>, the GPAC has recently been studied as a way to provide evidence for the <a href="/facts/Church%25E2%2580%2593Turing_thesis/hDHn641f">physical Church–Turing thesis</a>. This is because the GPAC is also known to model a large class of <a href="/facts/Dynamical_system/782gREl5">dynamical systems</a> defined with <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">ordinary differential equations</a>, which appear frequently in the context of <a href="/facts/Physics/a7aH2y08">physics</a>. In particular it was shown in 2007 that (a deterministic variant of) the GPAC is equivalent, in <a href="/facts/Computability/VpnJUkPN">computability</a> terms, to <a href="/facts/Turing_machine/ojCtglYu">Turing machines</a>, thereby proving the physical Church–Turing thesis for the class of systems modelled by the GPAC.
This was recently strengthened to <a href="/facts/Polynomial_time/77T62gmf">polynomial time</a> equivalence.
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General purpose analog computer open-in-new

General purpose analog computer