Complexity and real computation
Complexity and real computation
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
Computable analysis: an introduction
Iteration, inequalities, and differentiability in analog computers
Journal of Complexity
Introduction to Computability
Abstract versus concrete computation on metric partial algebras
ACM Transactions on Computational Logic (TOCL)
Real recursive functions and their hierarchy
Journal of Complexity
Computability over an arbitrary structure: sequential and parallel polynomial time
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Universality, reducibility, and completeness
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
The church-turing thesis over arbitrary domains
Pillars of computer science
| Hi-index | 0.00 |
We argue that there is currently no satisfactory general framework for comparing the extensional computational power of arbitrary computational models operating over arbitrary domains. We propose a conceptual framework for comparison, by linking computational models to hypothetical physical devices. Accordingly, we deduce a mathematical notion of relative computational power, allowing the comparison of arbitrary models over arbitrary domains. In addition, we claim that the method commonly used in the literature for “strictly more powerful” is problematic, as it allows for a model to be more powerful than itself. On the positive side, we prove that Turing machines and the recursive functions are “complete” models, in the sense that they are not susceptible to this anomaly, justifying the standard means of showing that a model is “hypercomputational.”