Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
The confluence of ideas in 1936
A half-century survey on The Universal Turing Machine
Recipes, Algorithms, and Programs
Minds and Machines
Computation: finite and infinite machines
Computation: finite and infinite machines
Minds and Machines
Physical Computation: How General are Gandy's Principles for Mechanisms?
Minds and Machines
Concrete Digital Computation: What Does it Take for a Physical System to Compute?
Journal of Logic, Language and Information
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We sketch the historical and conceptual context of Turing's analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland's views.