On the rapid computation of various polylogarithmic constants
Mathematics of Computation
Introduction to the Theory of Computation
Introduction to the Theory of Computation
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
Super-tasks, accelerating Turing machines and uncomputability
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Hypercomputation by definition
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Minds and Machines
Zeno machines and hypercomputation
Theoretical Computer Science
Conceptual Mathematics: A First Introduction to Categories
Conceptual Mathematics: A First Introduction to Categories
First Steps in Synthetic Computability Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Possibilities of Hypercomputing Supertasks
Minds and Machines
| Hi-index | 0.00 |
Hypercomputation--the hypothesis that Turing-incomputable objects can be computed through infinitary means--is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise irrelevant, since diagonalization can cover any amount of value assignments. This should not be construed as a restriction of computing power: Turing's uncomputability is not a `barrier' to be broken, but simply an effect of the expressive power of consistent programming systems.