Oracles and Advice as Measurements

Authors:
Edwin Beggs;José Félix Costa;Bruno Loff;John V. Tucker
Affiliations:
School of Physical Sciences, Swansea University, Wales, United Kingdom SA2 8PP;Department of Mathematics, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal and Centro de Matemática e Aplicações Fundamentais do Complexo Inte ...;Department of Mathematics, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal and Centro de Matemática e Aplicações Fundamentais do Complexo Inte ...;School of Physical Sciences, Swansea University, Wales, United Kingdom SA2 8PP
Venue:
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Year:
2008

Citing 6
Cited 2

Neural networks and analog computation: beyond the Turing limit

Neural networks and analog computation: beyond the Turing limit
Computable functions and semicomputable sets on many-sorted algebras

Handbook of logic in computer science
Abstract versus concrete computation on metric partial algebras

ACM Transactions on Computational Logic (TOCL)
On the complexity of measurement in classical physics

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Algorithmic randomness, quantum physics, and incompleteness

MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Computational power of neural networks: a characterization in terms of Kolmogorov complexity

IEEE Transactions on Information Theory

Limits to measurement in experiments governed by algorithms†

Mathematical Structures in Computer Science
The impact of models of a physical oracle on computational power

Mathematical Structures in Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we will try to understand how oracles and advice functions, which are mathematical abstractions in the theory of computability and complexity, can be seen as physical measurements in Classical Physics. First, we consider how physical measurements are a natural external source of information to an algorithmic computation, using a simple and engaging case study, namely: Hoyle's algorithm for calculating eclipses at Stonehenge. Next, we argue that oracles and advice functions can help us understand how the structure of space and time has information content that can be processed by Turing machines. Using an advanced case study from Newtonian kinematics, we show that non-uniform complexity is an adequate framework for classifying feasible computations by Turing machines interacting with an oracle in Nature, and that by classifying the information content of such a natural oracle, using Kolmogorov complexity, we obtain a hierarchical structure based on measurements, advice classes and information.