Hilbert's tenth problem
Communicating and mobile systems: the &pgr;-calculus
Communicating and mobile systems: the &pgr;-calculus
Automata, Languages, and Machines
Automata, Languages, and Machines
PI-Calculus: A Theory of Mobile Processes
PI-Calculus: A Theory of Mobile Processes
Computation and Hypercomputation
Minds and Machines
A Computer Scientist's View of Life, the Universe, and Everything
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
Algorithmic Theories of Everything
Algorithmic Theories of Everything
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Can general relativistic computers break the turing barrier?
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
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According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true, or do behaviours exist which are strictly hypercomputational? Several idealised computational models are known which suggest the possibility of hypercomputation, some Newtonian, some based on cosmology, some on quantum theory. While these models' physicality is debatable, they nonetheless throw into question the validity of extending CTT to include all physical systems. We consider the physicality of hypercomputational behaviour from first principles, by showing that quantum theory can be reformulated in a way that explains why physical behaviours can be regarded as `computing something' in the standard computational state-machine sense. While this does not rule out the physicality of hypercomputation, it strongly limits the forms it can take. Our model also has physical consequences; in particular, the continuity of motion and arrow of time become theorems within the basic model.