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}
}
  • M. Ziegler
  • Published 9 May 2008
  • Computer Science, Physics, Mathematics
  • Appl. Math. Comput.
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… 
The Physical Church-Turing Thesis and the Principles of Quantum Theory
TLDR
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.
Around the Physical Church-Turing Thesis: Cellular Automata, Formal Languages, and the Principles of Quantum Theory
TLDR
The physical Church-Turing thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature, putting the emphasis on the principle of a bounded density of information.
On More or Less Appropriate Notions of 'Computation'
TLDR
This paper presents some arguments about which notions of “computation” may be considered “reasonably acceptable” for the authors' own historic era, and emphasizes that every science-philosophical notion has its own long-term historical semantics which cannot be fixed once and forever.
Physical Oracles: The Turing Machine and the Wheatstone Bridge
TLDR
The theory proposes that measurability in Physics is subject to laws which are co-lateral effects of the limits of computability and computational complexity.
Unconventional Algorithms: Complementarity of Axiomatics and Construction
TLDR
This paper explains how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity, and demonstrates how new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation allow efficient navigation in the algorithmmic multiverse.
Limits to measurement in experiments governed by algorithms†
TLDR
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.
The impact of models of a physical oracle on computational power†
TLDR
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.
Complexity and Approximation: In Memory of Ker-I Ko
TLDR
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.
Logical Limitations to Machine Ethics with Consequences to Lethal Autonomous Weapons
TLDR
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.
...
1
2
3
...

References

SHOWING 1-10 OF 135 REFERENCES
Classical physics and the Church--Turing Thesis
  • A. Yao
  • Computer Science
    JACM
  • 2003
TLDR
In this article, it is observed that there is fundamental tension between the Extended Church--Turing Thesis and the existence of numerous seemingly intractable computational problems arising from classical physics.
Non-Turing Computations Via Malament–Hogarth Space-Times
We investigate the Church–Kalmár–Kreisel–Turing theses theoretical concerning (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general
Relativistic Computers and Non-uniform Complexity Theory
TLDR
In a complexity-theoretic analysis, it is shown that the (infinite) computations of S(n)-space bounded relativistic Turing machines are equivalent to (finite) Computations of Turing machines that use a S( n)- bounded advice f, which bounds the power of polynomial-space bounded relativity Turing machines by TM/poly.
Hypercomputation: computing more than the Turing machine
  • Toby Ord
  • Mathematics, Computer Science
    ArXiv
  • 2002
TLDR
Much of the work that has been done on hypercomputation is surveyed, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers.
Physics and metaphysics looks at computation
As far as algorithmic thinking is bound by symbolic paper-and-pencil operations, the Church-Turing thesis appears to hold. But is physics, and even more so, is the human mind, bound by symbolic
Transcending the Limits of Turing Computability
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we
Quantum Algorithm for Hilbert's Tenth Problem
  • T. Kieu
  • Mathematics, Physics
    ArXiv
  • 2001
TLDR
It is argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.
A Constructivist Manifesto for the Physical Sciences — Constructive Re-Interpretation of Physical Undecidability
Virtual physics is the study of the intrinsic perception of computer-generated universes. Algorithmic physics is the study of physical systems by methods developed in formal logic and the computer
Church's thesis meets the N-body problem
TLDR
This work points out that with any particular set of physical laws, Church’s thesis need not merely be postulated, in fact it may be decidable, and proves a useful theorem: a wide class of ordinary differential equations may be integrated with “polynomial slowdown”.
...
1
2
3
4
5
...