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Computations via experiments with kinematic systems
, 2004
"... Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be des ..."
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Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be designed to operate under (a) Newtonian mechanics or (b) Relativistic mechanics. The theorem proves that valid models of mechanical systems can compute all possible functions on discrete data. The proofs show how any information (coded by some A) can be embedded in the structure of a simple kinematic system and retrieved by simple observations of its behaviour. We reflect on this undesirable situation and argue that mechanics must be extended to include a formal theory for performing experiments, which includes the construction of systems. We conjecture that in such an extended mechanics the functions computed by experiments are precisely those computed by algorithms. We set these theorems and ideas in the context of the literature on the general problem “Is physical behaviour computable? ” and state some open problems.
Church’s Thesis and the Conceptual Analysis of Computability
 Notre Dame Journal of Formal Logic
, 2007
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UNIVERSITY OF PITTSBURGH FACULTY OF ARTS AND SCIENCES
, 2003
"... This dissertation was presented by ..."
Some Mathematical Methods and Tools for an Analysis of HarmonySeeking Computations
"... Summary. A general review of some topic concepts and methods of membrane computing [15], [19] which can be useful in an analysis of harmonyseeking computations [1] is presented. Then an application of a certain particular method of membrane computing in a discussion of mobility of some systems cons ..."
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Summary. A general review of some topic concepts and methods of membrane computing [15], [19] which can be useful in an analysis of harmonyseeking computations [1] is presented. Then an application of a certain particular method of membrane computing in a discussion of mobility of some systems considered in city planning [2] is described in some details. A conclusion of the discussion states that systems of hierarchical organization in a form of a tree are mobile by means of massively parallel (local) moves of the parts of the systems, where the moves are related to the process capabilities of moves of ambients in [7]. 1
Effective computation by humans and machines
, 2002
"... There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. ..."
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There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument for CTT by analyzing the processes carried out by a human computer. I then contend that if the Gandy–Sieg account is correct, then the notion of effective computability has changed after 1936. Today computer scientists view effective computability in terms of finite machine computation. My contention is supported by the current formulations of CTT, which always refer to machine computation, and by the current argumentation for CTT, which is different from the main arguments advanced by Turing and Church. I finally turn to discuss Robin Gandy’s characterization of machine computation. I suggest that there is an ambiguity regarding the types of machines Gandy was postulating. I offer three interpretations, which differ in their scope and limitations, and conclude that none provides the basis for claiming that Gandy characterized finite machine computation.