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.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference19 articles.
1. Classical computing, quantum computing, and Shor's factoring algorithm;Manin;Séminaire Bourbaki,1999
2. Causal nets or what is a deterministic computation?
3. Ebrahimi-Fard K. and Manchon D. (2007) The combinatorics of Bogolyubov's recursion in renormalization. (Available at arXiv0710.3675 [math-ph].)
4. Various measures of complexity for finite objects (axiomatic description);Levin;Soviet Math. Dokl.,1976
5. Most programs stop quickly or never halt
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献