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Renormalisation and computation II: time cut-off and the Halting Problem

Published online by Cambridge University Press:  06 September 2012

YURI I. MANIN*
Affiliation:
Max Planck Institut für Mathematik, Bonn, Germany and Northwestern University, Evanston, U.S.A.

Abstract

This is the second instalment in the project initiated in Manin (2012). In the first Part, we argued that both the philosophy and technique of perturbative renormalisation in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view.

In this second part, we address some of the issues raised in Manin (2012) and develop them further in three contexts: a categorification of the algorithmic computations; time cut-off and anytime algorithms; and, finally, a Hopf algebra renormalisation of the Halting Problem.

Type
Paper
Copyright
Copyright © Cambridge University Press 2012

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