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Computational complexity with experiments as oracles
, 2008
"... We discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of analogue-digital ma ..."
Abstract
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Cited by 10 (9 self)
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We discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of analogue-digital machine are studied, in which physical parameters can be set exactly and approximately. Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines. 1
Quanta in classical mechanics: uncertainty in space, time, energy (Extended Abstract)
- IN STUDIA LOGICA INTERNATIONAL CONFERENCE ON LOGIC AND THE FOUNDATIONS OF PHYSICS: SPACE, TIME AND QUANTA (TRENDS IN LOGIC VI
, 2008
"... Consider modelling an experiment intended to measure a quantity, such as position or mass in Classical Mechanics. A theoretical analysis of the process may examine the operations used in the experimental procedure and equipment, and explore relationships between the accuracy of the measurement and p ..."
Abstract
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Cited by 4 (4 self)
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Consider modelling an experiment intended to measure a quantity, such as position or mass in Classical Mechanics. A theoretical analysis of the process may examine the operations used in the experimental procedure and equipment, and explore relationships between the accuracy of the measurement and physical properties of the operations, such as their precision, and their use of time, space, and energy. How does the accuracy of measurements depend on resources? In a series of studies [5–7, 2, 1, 3] we have developed a methodology to investigate some fundamental notions about experimental methods in order to answer the question, What can one compute with a physical system? The methodology is based on defining experiments formally over some tightly specified theory T and analysing observable behaviours as the input-output of computations. The idea is (i) to understand the notion of computation inside a physical theory T in a way that is independent of classical computability theory of algorithms; and
Non-classical computing: feasible versus infeasible.
"... Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are ..."
Abstract
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Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future. The Infinite Improbability Drive is a wonderful new method of crossing vast interstellar distances in a mere nothingth of a second, without all that tedious mucking about in hyperspace.Adams & Stamp (1997) 1.
