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14
Computational complexity with experiments as oracles
, 2008
"... We discuss combining physical experiments with machine computations and introduce a form of analoguedigital 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 analoguedigital ma ..."
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Cited by 15 (10 self)
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We discuss combining physical experiments with machine computations and introduce a form of analoguedigital 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 analoguedigital machine are studied, in which physical parameters can be set exactly and approximately. Using nonuniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines. 1
THE PHYSICAL CHURCHTURING THESIS AND THE PRINCIPLES OF QUANTUM THEORY
, 2012
"... As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is ..."
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Cited by 5 (2 self)
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As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information — and proves that the physical ChurchTuring thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal nontrivial interplay between theoretical physics symmetries and computability assumptions.
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 ..."
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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 inputoutput 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
Representing measurement results
 In Brattka, V. et al. (eds) “Conference on Computability and Complexity in Analysis”, Informatik Berichte 348, FernUniversität Hagen (2008), 187
"... Abstract: To gain insight into the relationship between physical theories and computation, we examine the link between measurement devices and computers in the framework of TTE. Starting from a formal definition of a measurement procedure, different approaches to associate a representation with a me ..."
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Cited by 3 (3 self)
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Abstract: To gain insight into the relationship between physical theories and computation, we examine the link between measurement devices and computers in the framework of TTE. Starting from a formal definition of a measurement procedure, different approaches to associate a representation with a measurement procedure are studied, and an equivalence class of representations suitable for representing the results of a measurement is defined for each measurement procedure.
Five views of hypercomputation
"... We overview different approaches to the study of hypercomputation and other investigations on the plausibility of the physical Church–Turing thesis. We propose five thesis to classify investigation in this area. Sly does it. Tiptoe catspaws. Slide and creep. ..."
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Cited by 2 (0 self)
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We overview different approaches to the study of hypercomputation and other investigations on the plausibility of the physical Church–Turing thesis. We propose five thesis to classify investigation in this area. Sly does it. Tiptoe catspaws. Slide and creep.
Nonclassical 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 ..."
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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.
Transfinite Machine Models
, 2011
"... In recent years there has emerged the study of discrete computational models which are allowed to act transfinitely. By ‘discrete ’ we mean that the machine models considered are not analogue machines, but compute by means of distinct stages or in units of time. The paradigm of such models is, of co ..."
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In recent years there has emerged the study of discrete computational models which are allowed to act transfinitely. By ‘discrete ’ we mean that the machine models considered are not analogue machines, but compute by means of distinct stages or in units of time. The paradigm of such models is, of course, Turing’s original