Omnipotent Training

Before exploring the optimization problems with the assumption of omnipotence and omniscience, it is worthwhile to ask whether such a problem is of practical use or is merely an academic exercise. This molecular electronics project is currently in the proof-of-concept phase. Before determining whether it is possible to train a NanoCell with realistic constraints, we are attempting to verify whether it is theoretically possible. If it becomes clear that it is impossible to train a randomly assembled NanoCell as a 2-bit adder, even with the assumptions of omnipotence and omniscience, then there is no point in trying to train one without these simplifying assumptions. Hence, the optimization problem with the supposition of omnipotence is of practical use. 

In the optimization problem with omnipotence, we are given the graph within the NanoCell along with the I(V) curve of the molecule, the target logic device and settings of the I/O pins (i.e., which are set to input and output). The search space is all possible combinations of switch, or edge states. Simply stated, the problem then is  

Given the graph of the NanoCell G, the I(V) curve of the molecule, the target logic device and the settings of the I/O pins, 

Here / involves two steps (1) evaluate the output currents and (2) compare these currents against the desired logic. 

The simplified NanoCell training problem is particularly well suited to genetic algorithms. After presenting the fundamentals of genetic algorithms, a heuristic for solving this optimization problem is presented. 

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Before we began simulating the training of NanoCells, no one knew whether anything useful could be done with a random array of NDR devices. With the NanoCell simulator, we have shown that in fact NanoCells can be trained as fairly complex logical devices with the simplifying assumption of omnipotent training. 

Although, the problem of omnipotently training a NanoCell has been thoroughly explored in this chapter, there are still some potential improvements that should be explored. In the next section the issue of hooking NanoCells together is addressed. 

In this section, various areas of future research are discussed. First improvements in training individual NanoCells are covered, and then strategies for hooking NanoCells together are addressed. This is followed by a section on dropping the assumption of omnipotence for more realistic mortal training. The section concludes with the subject of proofs concerning trainability. 

The NanoCell training to date has been conducted under the assumption of omnipotence. However, NanoCells will be trained in a mortal fashion, so it is essential that mortal techniques be investigated in the near future. This is an issue that we are exploring. 

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