Dyson-Schwinger equations in the theory of computation

I will recall a set of analogies between quantum field theory and the theory of computation,
which allow for the formulation of a renormalization procedure for the halting problem,
by analogy with algebraic renormalization in perturbative quantum field theory, based on
Hopf algebras and Rota-Baxter algebras. I will focus on the role of equations of motion
in quantum field theory, formulated in terms of combinatorial Dyson-Schwinger equation
and the meaning of their counterpart in the theory of computation. The talk is based on joint
work with Colleen Delaney and on ongoing work with Joachim Koch.