Supertask computation
نویسنده
چکیده
Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.
منابع مشابه
Hypercomputation and the Physical Church-Turing Thesis
A version of the Church-Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines (‘Thesis P’); in this formulation the Thesis appears an empirical, more than a logico-mathematical, proposition. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal...
متن کاملInfinite Time Turing Machines With Only One Tape
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for functions f .. R → N, the same class of computable functions. Nevertheless, there are infinite time computable functions f : R → R that are not one-...
متن کاملA Quantum Mechanical Supertask
That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential SchroÈ dinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as a...
متن کاملul 1 99 9 Infinite time Turing machines with only one tape Joel
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for functions f .. R → N, the same class of computable functions. Nevertheless, there are infinite time computable functions f : R → R that are not one-...
متن کاملHypercomputation, Frege, Deleuze: Solving Thomson's Lamp
We present the first known solution to the original supertask, the Thomson Lamp Paradox. Supertasks, or infinite operations, form an integral part of the emerging study of hypercomputation (computation in excess of classical Turing machine capabilities) and are of philosophical interest for the paradoxes they engender. We also offer preliminary resources for classifying computational complexity...
متن کامل