On the computational power of dynamical systems and hybrid systems
Theoretical Computer Science - Special issue on universal machines and computations
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Classical physics and the Church--Turing Thesis
Journal of the ACM (JACM)
Can Newtonian systems, bounded in space, time, mass and energy compute all functions?
Theoretical Computer Science
Oracles and Advice as Measurements
UC '08 Proceedings of the 7th international conference on Unconventional Computing
On the complexity of measurement in classical physics
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Limits to measurement in experiments governed by algorithms†
Mathematical Structures in Computer Science
The ARNN model relativises P =NP and P≠NP
Theoretical Computer Science
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Using physical experiments as oracles for algorithms, we can characterise the computational power of classes of physical systems. Here we show that two different physical models of the apparatus for a single experiment can have different computational power. The experiment is the scatter machine experiment (SME), which was first presented in Beggs and Tucker (2007b). Our first physical model contained a wedge with a sharp vertex that made the experiment non-deterministic with constant runtime. We showed that Turing machines with polynomial time and an oracle based on a sharp wedge computed the non-uniform complexity class P/poly. Here we reconsider the experiment with a refined physical model where the sharp vertex of the wedge is replaced by any suitable smooth curve with vertex at the same point. These smooth models of the experimental apparatus are deterministic. We show that no matter what shape is chosen for the apparatus: the time of detection of the scattered particles increases at least exponentially with the size of the query; and Turing machines with polynomial time and an oracle based on a smooth wedge compute the non-uniform complexity class P/log* ? P/poly. We discuss evidence that many experiments that measure quantities have exponential runtimes and a computational power of P/log*.