Supertasks do not increase computational power

Oron Shagrir

doi:10.1007/s11047-011-9280-y

Supertasks do not increase computational power

Oron Shagrir

The Hebrew University of Jerusalem

Research output: Contribution to journal › Review article › peer-review

Abstract

It is generally assumed that supertasks increase computational power. It is argued, for example, that supertask machines can compute beyond the Turing limit, e.g., compute the halting function. We challenge this assumption. We do not deny that supertask machines can compute beyond the Turing limit. Our claim, rather, is that the (hyper) computational power of these machines is not related to supertasks, but to the "right kind" of computational structure.

Original language	English
Pages (from-to)	51-58
Number of pages	8
Journal	Natural Computing
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s11047-011-9280-y
State	Published - Mar 2012

Keywords

Accelerating Turing machines
Halting function
Hyper computation
Relativistic machines
Supertasks
Turing machines

All Science Journal Classification (ASJC) codes

Computer Science Applications

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10.1007/s11047-011-9280-y

Cite this

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title = "Supertasks do not increase computational power",

abstract = "It is generally assumed that supertasks increase computational power. It is argued, for example, that supertask machines can compute beyond the Turing limit, e.g., compute the halting function. We challenge this assumption. We do not deny that supertask machines can compute beyond the Turing limit. Our claim, rather, is that the (hyper) computational power of these machines is not related to supertasks, but to the {"}right kind{"} of computational structure.",

keywords = "Accelerating Turing machines, Halting function, Hyper computation, Relativistic machines, Supertasks, Turing machines",

author = "Oron Shagrir",

note = "Funding Information: Acknowledgments Thanks to the participants of the Workshop on Physics and Computation at Ponta Delgada (2009) and to three anonymous referees for corrections and suggestions. This research was supported by the Israel Science Foundation, grant 725/08.",

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AB - It is generally assumed that supertasks increase computational power. It is argued, for example, that supertask machines can compute beyond the Turing limit, e.g., compute the halting function. We challenge this assumption. We do not deny that supertask machines can compute beyond the Turing limit. Our claim, rather, is that the (hyper) computational power of these machines is not related to supertasks, but to the "right kind" of computational structure.

KW - Accelerating Turing machines

KW - Halting function

KW - Hyper computation

KW - Relativistic machines

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SP - 51

EP - 58

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JF - Natural Computing

IS - 1

ER -

Supertasks do not increase computational power

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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