NDLI: Output concepts for accelerated Turing machines

Content Provider	Springer Nature Link
Author	Potgieter, Petrus H. Rosinger, Elemér E.
Copyright Year	2010
Abstract	The accelerated Turing machine (ATM) is the work-horse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discussion of either the possible actual use by such a machine of an infinite amount of space, or the difficulty (even if only a finite amount of space is used) of defining an outcome for machines acting like Thomson’s lamp. It is the authors’ impression that insufficient attention has been paid to introducing a clearly defined counterpart for ATMs of the halting/non-halting dichotomy for classical Turing computation. This paper tackles the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. Non-standard integers appear quite useful in this regard and we describe several models of computation using filters.Die versnelde Turing-masjien (VTM) is die trekperd van hiperberekening. In sekere gevalle word veronderstel dat ’n masjien wat aftelbaar oneindig aantal stappe uitgevoer het, ’n interessante probleem soos die Tweelingpriemvermoede sou beslis het. ’n Mens lê egter sorg aan die dag om ’n uiteensetting van òf die potensiële benutting van oneindig veel ruimte deur ’n dergelike masjien òf die probleem (indien slegs eindig veel ruimte gebruik is) om ’n eindtoestand te definieer vir masjiene wat optree soos Thomson se lamp. Die outeurs is onder die indruk dat te min aandag gegee word aan die invoer van ’n deeglik gedefinieerde eweknie van die halt/niehalt-tweespalt in klassieke Turing-berekening. Hierdie artikel takel die probleem van definisie van die uitvoer, of finale boodskap, van ’n masjien wat ’n aftelbaar oneindige aantal stappe uitgevoer het. Die niestandaard-heelgetalle skyn nuttig te wees in hierdie verband en ons beskryf ’n aantal berekeningsmodelle met filters.
Starting Page	853
Ending Page	864
Page Count	12
File Format	PDF
ISSN	15677818
Journal	Natural Computing
Volume Number	9
Issue Number	4
e-ISSN	15729796
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-04-16
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Accelerated Turing machine Zeno machine Non-standard output concepts Ultrafilter accepting computations Thomson’s lamp Statistical Physics, Dynamical Systems and Complexity Artificial Intelligence (incl. Robotics) Processor Architectures Evolutionary Biology Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Supertasks do not increase computational power

Complexity-preserving simulations among three variants of accepting networks of evolutionary processors

Abstract geometrical computation 5: embedding computable analysis

Doubles and negatives are positive (in self-assembly)

Turing patterns with Turing machines: emergence and low-level structure formation

On the complexity of nonuniform wavelength-based machine

Computation in Sofic Quantum Dynamical Systems

A survey of recursive analysis and Moore’s notion of real computation

Programmable reconfiguration of Physarum machines

Output concepts for accelerated Turing machines

Similar Documents

Supertasks do not increase computational power

Complexity-preserving simulations among three variants of accepting networks of evolutionary processors

Abstract geometrical computation 5: embedding computable analysis

Doubles and negatives are positive (in self-assembly)

Turing patterns with Turing machines: emergence and low-level structure formation

On the complexity of nonuniform wavelength-based machine

Computation in Sofic Quantum Dynamical Systems

A survey of recursive analysis and Moore’s notion of real computation

Programmable reconfiguration of Physarum machines

Output concepts for accelerated Turing machines