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Okay, I think this makes sense. The idea is trying to re-interpret the various functions in the utility function as a single function and asking about the notion of complexity on that function which combines the complexity of producing a circuit which computes that function and the complexity of the circuit itself.

But just to check: is T over  $S\times A\times O\to S$? I thought T in utility functions only depended on states and actions $S\times A\to S$? 

Maybe I am confused by what you mean by $S$. I thought it was the state space, but that isn't consistent wit... (read more)

I am not sure I understand your use of $C\left(U\right)$ in the third from last paragraph where you define goal directed intelligence. As you define $C$ it is a complexity measure over programs $P$. I assume this was a typo and you mean $K\left(U\right)$? Or am I misunderstanding the definition of either $U$ or $C$?

Is there a place to look for papers and posts people have already submitted (and want to be public)?