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Article Dans Une Revue Philosophia Mathematica Année : 2023

On Algorithms, Effective Procedures, and Their Definitions

Résumé

I examine the classical idea of 'algorithm' as a sequential, step-by-step, deterministic procedure (i.e., the idea of 'algorithm' that was already in use by the 1930s), with respect to the following themes: (a) its relation to the notion of an 'effective procedure', (b) its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and (c) its different formal definitions proposed by practitioners in these areas. I argue that 'algorithm' has been conceptualized and used in contrasting ways in the above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) 'algorithms'.
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Dates et versions

hal-04420362 , version 1 (13-02-2024)

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Philippos Papayannopoulos. On Algorithms, Effective Procedures, and Their Definitions. Philosophia Mathematica, 2023, 31 (3), pp.291-329. ⟨10.1093/philmat/nkad011⟩. ⟨hal-04420362⟩
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