# Physically-relativized Church-Turing Hypotheses: Physical foundations of computing and complexity theory of computational physics

@article{Ziegler2009PhysicallyrelativizedCH, title={Physically-relativized Church-Turing Hypotheses: Physical foundations of computing and complexity theory of computational physics}, author={Martin Ziegler}, journal={Appl. Math. Comput.}, year={2009}, volume={215}, pages={1431-1447} }

We turn the physical Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies and causes for misunderstanding concerning the state of the Church-Turing Hypothesis (CTH), it is suggested to study the CTH 'sharpened' relative to an arbitrary but specific physical theory - rather than vaguely referring to ''nature'' in general. For this purpose we apply, and emphasize the…

## 22 Citations

The Physical Church-Turing Thesis and the Principles of Quantum Theory

- Computer Science, PhysicsInt. J. Found. Comput. Sci.
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This approach exhibits a formal non-trivial interplay between theoretical physics symmetries and computability assumptions, and provides a quantum version of the Church-Turing theorem.

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The theory proposes that measurability in Physics is subject to laws which are co-lateral effects of the limits of computability and computational complexity.

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- Computer Science, MathematicsMathematical Structures in Computer Science
- 2010

This paper specifies an experiment that measures mass via collisions in Newtonian dynamics and examines its properties in preparation for its use as an oracle, and begins the classification of the computational power of polynomial time Turing machines with this experimental oracle using non-uniform complexity classes.

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The impact of models of a physical oracle on computational power†

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Two different physical models of the apparatus for a single experiment can have different computational power, using physical experiments as oracles for algorithms to characterise the computational power of classes of physical systems.

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A detailed discussion of Ker-I Ko’s work on the question of whether it is NP-hard to determine the time-bounded Kolmogorov complexity of a given string is included, which is closely connected with the Minimum Circuit Size Problem (MCSP), which is central to several contemporary investigations in computational complexity theory.

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This work employs mathematical logic and theoretical computer science to explore fundamental limitations to the moral behaviour of intelligent machines in a series of "Gedankenexperiments" and constructs an (admittedly artificial but) fully deterministic situation where a robot is presented with two choices -- yet it provably cannot decide algorithmically which one.

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