Abstract
Abstract
We describe a novel machine model of computation, and prove that this model is capable of performing calculations beyond the capability of the standard Turing machine model. In particular, we demonstrate the ability of our model to solve the Halting problem for Turing machines. We discuss the issues involved in implementing the model as a physical device, and offer some tentative suggestions.
- [Cou54] Coulson, C. A.:Electricity. Oliver and Boyd, 1954.Google Scholar
- [Cro76] Cross, R. C.:Electricity and Magnetism. Longman, 1976.Google Scholar
- [Cut80] Cutland, N. J.:Computability. Cambridge University Press, 1980.Google Scholar
- [Deu85] Quantum Theory, the Church-Turing Principle and the Universal Quantum ComputerProc. Royal Soc.1985A40087117Google Scholar
- [Deu89] Deutsch, D.: Quantum Communication Thwarts Eavesdroppers.New Scientist, 9 December (1989).Google Scholar
- [Ei174] Eilenberg, S.:Automata, Languages, and Machines, vol. A. Academic Press, 1974.Google Scholar
- [Ho187] Formal Methods in the Specification of the Human-Computer InterfaceInt. CIS J.1987122436Google Scholar
- [Ho188] X-machines as a Basis for System SpecificationSoft. Eng. J.1988326976Google ScholarDigital Library
- [Pen89] Penrose, R.:The Emperor's New Mind. Oxford University Press, 1989.Google Scholar
- [RoB81] Roberts, A. and Bush, B. (eds):Neurones without Impulses. Cambridge University Press, 1981.Google Scholar
- [Wei73] Weir, A. J.:Lebesgue Integration and Measure. Cambridge University Press, 1973.Google Scholar
- [Wi170] Willard, S.:General Topology. Addison-Wesley, 1970.Google Scholar
Index Terms
- X-machines and the halting problem: Building a super-turing machine
Recommendations
Weak synchronization and synchronizability of multi-tape pushdown automata and turing machines
Given an n-tape automaton M with a one-way read-only head per tape which is delimited by an end marker $ and a nonnegative integer k, we say that M is weakly k-synchronized if for every n-tuple x = (x1,..., xn) that is accepted, there is an accepting ...
On the Generic Undecidability of the Halting Problem for Normalized Turing Machines
Hamkins and Miasnikov presented in (Notre Dame J. Formal Logic 47(4), 515---524, 2006) a generic algorithm deciding the classical Halting Problem for Turing machines with one-way tape on a set of asymptotic probability one (on a so-called generic set). ...
Weak synchronization and synchronizability of multitape pushdown automata and turing machines
LATA'12: Proceedings of the 6th international conference on Language and Automata Theory and ApplicationsGiven an n-tape automaton M with a one-way read-only head per tape which is delimited by an end marker $ and a nonnegative integer k, we say that M is weakly k-synchronized if for every n-tuple x=(x1, …, xn) that is accepted, there is an accepting ...
Comments