Turing machines can be efficiently simulated by the General Purpose Analog Computer
Amaury Pouly, Olivier Bournez, Daniel S. Gra\c{c}a

TL;DR
This paper demonstrates that Turing machine computations can be efficiently simulated by the General Purpose Analog Computer (GPAC) at a complexity level comparable to classical models, bridging a gap in understanding analog computation.
Contribution
It shows, for the first time, that GPACs can simulate Turing machines efficiently at a complexity level, extending the Church-Turing thesis to analog models.
Findings
GPAC simulations are space-efficient for bounded computations
Turing computations can be polynomially reduced to GPAC computations
Establishes a complexity-level equivalence between GPAC and classical models
Abstract
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity…
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