I am interested in the relation between "program complexity" and "computational complexity".
In particular, I was wondering
What is known about the minimal length a program must have to solve a given problem (efficiently)?
Is there such thing as "program complexity-bounded" computational complexity classes?
Any information related to the topic is much appreciated. Is this an active research area? What are open problems? References to textbooks, research articles? etc.
(Googling this, all I find is "resource-bounded Kolmogorov complexity" etc., but that seems to be the exact opposite of what I am looking for...)
EDIT: Some context: In the field I am working in the argument "simple algorithms cannot possibly perform as good as complex ones", is often quoted to motivate unnecessarily complex approaches. While this is by itself an insufficient argument, I can understand that some problems indeed might require a minimal complexity to be solved (efficiently?). However, I was wondering whether there were any general theoretical results supporting this notion, or research being performed in this direction.