Approximate Outputs of Accelerated Turing Machines Closest to Their Halting Point
The accelerated Turing machine (ATM) which can compute super-tasks are devices with the same computational structure as Turing machines (TM) and they are also defined as the work-horse of hypercomputation. Is the final output of the ATM can be produced at the halting state? We supported our analysis by reasoning on Thomson’s paradox and by looking closely the result of the Twin Prime conjecture. We make sure to avoid unnecessary discussion on the infinite amount of space used by the machine or considering Thomson’s lamp machine, on the difficulty of specifying a machine’s outcome. Furthermore, it’s important for us that a clear definition counterpart for ATMs of the non-halting/halting dichotomy for classical Turing must be introduced. Considering a machine which has run for a countably infinite number of steps, this paper addresses the issue of defining the output of a machine close or at the halting point.
KeywordsThomson’s paradox Super-task Halting problem Ultrafilter accepting computations Accelerating turing machines Non-standard output concepts
The work and the contribution were supported by the SPEV project “Smart Solutions in Ubiquitous Computing Environments”, 2019, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic.
- 4.Hamkins, J.D., Seabold, D.E.: Infinite time turing machines with only one tape. Math. Log. Q. 47, 271–287 (2001). https://doi.org/10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6MathSciNetzbMATHGoogle Scholar
- 8.Copeland, B., Shagrir, O.: Do accelerating turing machines compute the uncomputable. Mind. Mach. 21(2), 221–239 (2011)Google Scholar
- 13.Pitowsky, I.: The physical church thesis and physical computational complexity. Iyyun: Jerusalem Philos. Q. 39, 81–99 (1990)Google Scholar
- 14.Turing, A.: On Computable Numbers, with an Application to. http://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
- 16.How Light Bulbs Work. In: HowStuffWorks. https://home.howstuffworks.com/light-bulb.htm
- 17.Circuits and the Speed of Light. In: allaboutcircuits. https://www.allaboutcircuits.com/textbook/alternating-current/chpt-14/circuits-and-the-speed-of-light/
- 18.Graves, A., Wayne, G., Danihelka, I.: Neural turing machines. arXiv: Neural and Evolutionary Computing (2014)Google Scholar
- 19.Mambou, S., Krejcar, O., Kuca, K., Selamat, A.: Novel cross-view human action model recognition based on the powerful view-invariant features technique. Future Internet 10(9), 89 (2018)Google Scholar
- 20.Mambou, S., Maresova, P., Krejcar, O., Selamat, A., Kuca, K.: Breast cancer detection using infrared thermal imaging and a deep learning model. Sensors 18, 2799 (2018)Google Scholar