Renormalization and Computation II: Time Cut-off and the Halting Problem

Details Renormalization and Computation II: Time Cut-off and the Halting Problem Renormalization and Computation II: Time Cut-off and the Halting Problem

2009-08-24

arxiv.org/abs/0908.3430v1

Mathematics

Quantum Algebra

28 pages

Scientific paper

This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view. In this second part, I address some of the issues raised in [Ma3] and provide their development in three contexts: a categorification of the algorithmic computations; time cut--off and Anytime Algorithms; and finally, a Hopf algebra renormalization of the Halting Problem.

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