Complexity - Special issue on uncoventional models of computation
Field computation in natural and artifical intelligence
Information Sciences: an International Journal
Stochastic analog networks and computational complexity
Journal of Complexity
Communication and Concurrency
Matter and Consciousness
Field Computation: A Theoretical Framework for Massively Parallel Analog Computation
Field Computation: A Theoretical Framework for Massively Parallel Analog Computation
Hypercomputation: philosophical issues
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Evolved Computing Devices and the Implementation Problem
Minds and Machines
The computational status of physics
Natural Computing: an international journal
ICCS'11 Proceedings of the 19th international conference on Conceptual structures for discovering knowledge
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Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe.