Turing's analysis of computability, and major applications of it
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Computability and logic
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Elements of the Theory of Computation
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Algorithmics: The Spirit of Computing
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Two Dogmas of Computationalism
Minds and Machines
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Physical Hypercomputation and the Church–Turing Thesis
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Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Minds and Machines
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From Logic to Physics: How the Meaning of Computation Changed over Time
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
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Minds and Machines
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Foundational analyses of computation
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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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.