I think you are asking about two different things.
The ability of a programming language to represent all its programs as data.
Reasoning about programs as data.
For analytical purposes it's useful to keep them apart. I will focus on the former.
The ability of a
programming languages to represent, manipulate (and run) its programs
as data goes ...
No there is no current system that does all four steps in your system. If you want to design a system one of the first requirements is homoiconic language. At minimum you would want your core programming language that you have as small as possible so that when you enter the system and start to make it interpret itself it will work. So therefore you want a ...
As @user217281728's answer mentions there are a type of machines related more to inference and AI, called Gödel Machines
A Gödel machine is a self-improving computer program invented by
Jürgen Schmidhuber that solves problems in an optimal way. It uses a
recursive self-improvement protocol in which it rewrites its own code
when it can prove the new ...
In stats I think they'd say "imputation". CS theorists might model this as "matrix completion" (if you make it a matrix), "collaborative filtering" (like in the Netflix challenge). Maybe others know of more keywords.
First of all, there is a lot of information in this related question: Max Min of function less than Min max of function.
That said, the source of your problem is a confusion about which choices are available to each player when it is their turn. Consider the left-hand side of your first example: writing this in matrix form, each player gets to choose ...
Your question is underspecified.
If you just want to fill the gaps, put some fixed arbitrary value there.
To make the question interesting you have to specific some condition for preferring one way of filling the gaps vs. another one.
Essentially what metric are you trying to optimize?
E.g. are you assuming that your data is a sample coming from some ...
The question has changed somewhat in the comments, so I'll address its new version: "Given a class of algorithms $A$ and an $\epsilon >0$ and a loss class $L$ and a data distribution $D$, one cannot use algorithms of type $A$ to find a member of $L$ whose generalization error is below $\epsilon$ unless running time is $f(\epsilon)$"... .
One such lower ...
I suppose the scientific consensus is that while we are very far from there, in principle a digital artificial intelligence could mimic a human intelligence.
For some recent work on the Church-Turing thesis and the relation between physical computation and digital computation by Turing machines, see:
Space Bounded Church-Turing thesis and computational ...
You are probably speaking about something like a process ontology. Lately, that research has focused (moved?) on semantic workflows, e.g. to model processes in science, related with reproducibility. Similarly, we can also find the application of ontologies to business processes.
For more classical (lower level?) approaches, you may be interested in the ...
Let's assume all possible paths are finite to make the discussion simpler. This is the case for the vast majority of game actually played such as Chess (because of the 50-move rule) or Go (assuming superko is forbidden).
The idea you have about chosing the move maximizing the minimum path is actually an instance of the following more general idea. A proof ...
The maths involved in AI are not advanced, and are taught at the undergrad level. AI training and inferencing algorithms are in the domain of advanced Computer Science.
It is a bit of a word game. Some history should also be included when researching AI.
For example, in the current nomenclature, Deep Learning seems to be a trending keyword in AI.