Structural complexity 1
Structural complexity 2
The Busy Beaver Game and the meaning of life
The universal Turing machine (2nd ed.)
On the computational power of dynamical systems and hybrid systems
Theoretical Computer Science - Special issue on universal machines and computations
The structure of logarithmic advice complexity classes
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Can Newtonian systems, bounded in space, time, mass and energy compute all functions?
Theoretical Computer Science
Programming Experimental Procedures for Newtonian Kinematic Machines
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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
Communications of the ACM
The impact of models of a physical oracle on computational power
Mathematical Structures in Computer Science
The ARNN model relativises P =NP and P≠NP
Theoretical Computer Science
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We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment? In a programme to study the nature of computation possible by physical systems, and by algorithms coupled with physical systems, we have begun to analyse: (i)the algorithmic nature of experimental procedures; and(ii)the idea of using a physical experiment as an oracle to Turing Machines. To answer the question, we will extend our theory of experimental oracles so that we can use Turing machines to model the experimental procedures that govern the conduct of physical experiments. First, we specify an experiment that measures mass via collisions in Newtonian dynamics and examine its properties in preparation for its use as an oracle. We begin the classification of the computational power of polynomial time Turing machines with this experimental oracle using non-uniform complexity classes. Second, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on what can be measured using equipment. Indeed, the theorems suggest a new form of uncertainty principle for our knowledge of physical quantities measured in simple physical experiments. We argue that the results established here are representative of a huge class of experiments.