Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
SIAM Journal on Computing
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Coins, Quantum Measurements, and Turing's Barrier
Quantum Information Processing
Classical physics and the Church--Turing Thesis
Journal of the ACM (JACM)
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Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
Alan Turing: Life and Legacy of a Great Thinker
Alan Turing: Life and Legacy of a Great Thinker
Experience, generations, and limits in machine learning
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Hypercomputation with quantum adiabatic processes
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Hypercomputation: philosophical issues
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The church-turing thesis: breaking the myth
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Infinitary computability with infinite time turing machines
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Ultrafilter and Non-standard Turing Machines
UC '08 Proceedings of the 7th international conference on Unconventional Computing
On the Brightness of the Thomson Lamp: A Prolegomenon to Quantum Recursion Theory
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
A Brief Critique of Pure Hypercomputation
Minds and Machines
A note on accelerated turing machines
Mathematical Structures in Computer Science
On the Possibilities of Hypercomputing Supertasks
Minds and Machines
Computation as an unbounded process
Theoretical Computer Science
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This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is suggested that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded rôle of Turing computability in the mathematical sciences stands unchallenged.