Math. Structures Comput. Sci., 2012, Volume 22, Issue 5, Pages 729–751
Renormalisation and computation II: time cut-off and the Halting problem
Yu. I. Maninab
a Max Planck Institut für Mathematik, Bonn, Germany
b Northwestern University, Evanston, U.S.A.
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.
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