Concrete models of computation for topological algebras
Theoretical Computer Science - Special issue on computability and complexity in analysis
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
Computable analysis: an introduction
Computable functions and semicomputable sets on many-sorted algebras
Handbook of logic in computer science
Classical physics and the Church--Turing Thesis
Journal of the ACM (JACM)
The Complexity of N-body Simulation
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Is the Linear Schrödinger Propagator Turing Computable?
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Analog computers and recursive functions over the reals
Journal of Complexity
Abstract versus concrete computation on metric partial algebras
ACM Transactions on Computational Logic (TOCL)
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Abstract geometrical computation for black hole computation
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
A network model of analogue computation over metric algebras
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Physical constraints on hypercomputation
Theoretical Computer Science
(Short) Survey of Real Hypercomputation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Programming Experimental Procedures for Newtonian Kinematic Machines
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
On the complexity of measurement in classical physics
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Non-classical computing: feasible versus infeasible
Proceedings of the 2010 ACM-BCS Visions of Computer Science Conference
Limits to measurement in experiments governed by algorithms†
Mathematical Structures in Computer Science
The physical Church thesis as an explanation of the Galileo thesis
Natural Computing: an international journal
The impact of models of a physical oracle on computational power
Mathematical Structures in Computer Science
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In the theoretical analysis of the physical basis of computation there is a great deal of confusion and controversy (e.g., on the existence of hyper-computers). First, we present a methodology for making a theoretical analysis of computation by physical systems. We focus on the construction and analysis of simple examples that are models of simple sub-theories of physical theories. Then we illustrate the methodology by presenting a simple example for Newtonian Kinematics, and a critique that leads to a substantial extension of the methodology. The example proves that for any set A of natural numbers there exists a 3-dimensional Newtonian kinematic system M"A, with an infinite family of particles P"n whose total mass is bounded, and whose observable behaviour can decide whether or not n@?A for all n@?N in constant time. In particular, the example implies that simple Newtonian kinematic systems that are bounded in space, time, mass and energy can compute all possible sets and functions on discrete data. The system is a form of marble run and is a model of a small fragment of Newtonian Kinematics. Next, we use the example to extend the methodology. The marble run shows that a formal theory for computation by physical systems needs strong conditions on the notion of experimental procedure and, specifically, on methods for the construction of equipment. We propose to extend the methodology by defining languages to express experimental procedures and the construction of equipment. We conjecture that the functions computed by experimental computation in Newtonian Kinematics are ''equivalent'' to those computed by algorithms, i.e. the partial computable functions.