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A geometric theory of algorithms

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Authors : Seiller, Thomas (Author of the conference)
CIRM (Publisher )

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Abstract : In this programmatic talk, we will sketch both a conceptual and formal framework for reasoning about the notion of algorithm. This framework will arise from the analysis we will make of the relationships existing between the notion of algorithm and other similar (but still different) notions, like that of computation and that of program. We will first show that the Turing-Church thesis concerning effective computability is not sufficient to capture the notion of algorithm, as it identifies programs which are intensionally different. We will then show the limits of the existing models of computation in capturing some basic construction processes that we are willing to call algorithmic. In order to solve this problem, we propose a formalisation of the notion of model of computation on the base of which we claim that the notion of algorithm could eventually be analyzed. This approach centered around the dynamics of program execution, reconciles the more mechanical view of computation (such as formalized by Turing machines and automata) with the logical view - as it in particular stems from a generalization of Jean-Yves Girard's Geometry of Interaction programme.

MSC Codes :
00A30 - Philosophy of mathematics [See also 03A05]
03B47 - Substructural logics
03B70 - Logic of programming, See also {68Q55, 68Q60}
37N99 - None of the above
68Q05 - Models of computation (Turing machines, etc.)
68Q10 - Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 21/02/2022
    Conference Date : 11/02/2022
    Subseries : Research School
    arXiv category : Logic in Computer Science ; Dynamical Systems
    Mathematical Area(s) : Computer Science ; History of Mathematics ; Logic and Foundations ; Mathematics in Science & Technology
    Format : MP4 (.mp4) - HD
    Video Time : 00:49:42
    Targeted Audience : Researchers ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-02-11_Seiller.mp4

Information on the Event

Event Title : Logic and transdiciplinarity: Mathematics/Computer Science/ Philosophy/Linguistics / La Logique et la transdisciplinarite : Maths/Info/Philo/Linguistique
Event Organizers : Quatrini, Myriam ; Tortora de Falco, Lorenzo ; Vaux Auclair, Lionel
Dates : 07/02/2022 - 11/02/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2687.html

Citation Data

DOI : 10.24350/CIRM.V.19887403
Cite this video as: Seiller, Thomas (2022). A geometric theory of algorithms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19887403
URI : http://dx.doi.org/10.24350/CIRM.V.19887403

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