Dyson-Schwinger equations in the theory of computation

Abstract

Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of algorithms computing primitive and partial recursive functions and in the halting problem.

26 pages, LaTeX, final version, in "Feynman Amplitudes, Periods and Motives", Contemporary Mathematics, AMS 2015