Your definition of L-knowledge implies there can ‘only’ be O(2L) total possible latent variables in the universe that are L-knowable for any given L, I believe.
This isn’t strictly a problem, as you can just increase L… but your upper bound on L before the answer is trivially ‘yes’ is the inverse Kolmogorov complexity of the program trace + o(1). This grows slower than any computable function.
I’d be concerned that for programs of ‘realistic’ (read: ‘fits within the universe’) sizes there is no such L.
Your definition of L-knowledge implies there can ‘only’ be O(2L) total possible latent variables in the universe that are L-knowable for any given L, I believe.
This isn’t strictly a problem, as you can just increase L… but your upper bound on L before the answer is trivially ‘yes’ is the inverse Kolmogorov complexity of the program trace + o(1). This grows slower than any computable function.
I’d be concerned that for programs of ‘realistic’ (read: ‘fits within the universe’) sizes there is no such L.